A bibliography on spline functions - Pure - Aanmelden · September 1971 Technological University...
Transcript of A bibliography on spline functions - Pure - Aanmelden · September 1971 Technological University...
A bibliography on spline functions
Citation for published version (APA):van Rooij, P. L. J., & Schurer, F. (1971). A bibliography on spline functions. (EUT report. WSK, Dept. ofMathematics and Computing Science; Vol. 71-WSK-02). Eindhoven: Technische Hogeschool Eindhoven.
Document status and date:Published: 01/01/1971
Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication
General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:
www.tue.nl/taverne
Take down policyIf you believe that this document breaches copyright please contact us at:
providing details and we will investigate your claim.
Download date: 08. Aug. 2019
September 1971
Technological University Eindhoven Netherlands
Department of Mathematics
A BIBLIOGRAPHY ON SPLINE FUNCTIONS
by
P.L.J. vanRooy and F . Schurer
T.H. -Report 71-WSK-02
TECHNISCHE HOGESCHOOL EINDHOVEN
NEDERLAND
ONDERAFDELING DER WISKUNDE
TECHNOLOGICAL UNIVERSITY EINDHOVEN
THE NETHERLANDS
DEPARTMENT OF MATHEMATICS
A bibliography on spline functions
by
P.L.J. van Rooij and F. Schurer
T.H.-Report 71-WSK-02
October 1971
Introduction
This bibliography aims to be a reference to the knowledge concerning
the theory and application of spline functions. The main part consists of a
list which is ordered chronologically and, for publications that have ap
peared in the same year, alphabetically. Moreover, there is an index of
authors together with a coded list of the papers they have contributed to
the field.
This compilation of spline literature includes three kinds of publica
tions, namely papers in mathematical periodicals, books and doctoral disser
tations, all of which have appeared before January l, 1971. We remark that a
fourth kind of publication, reports, has been deleted from the bibliography.
There are various reasons for this omission.
(i) There is a wide variety in the status and quality of reports. Some of
them are meant only for internal use whereby the communicated results
are occasionally not yet in their definite form. Moreover, what is
really worthwhile will sooner or later be published in the current
mathematical journals.
(ii) Although it would be relatively easy to give a long and impressive list
of reports (one only needs to think of the large number of reports
issued on the subject by the Mathematics Research Center at the Uni
versity of Wisconsin), it no doubt would be a formidable task to give a
representative survey of the literature existing in this form. A good
deal of these publications is hard to retrieve and the distribution is
often very limited. Therefore, we do not feel qualified to make an at
tempt in this direction.
Besides this list, there are several other sources where one can find
elaborate references to the literature on spline functions. In this respect
we want to mention the bibliographies in the monograph of Ahlberg, Nilson
and Walsh [67 - 2] and in the books edited respectively by Greville
[69 - 24] and Schoenberg [69 - 69]. Other useful information is cor1tained in
the bibliography "Recent publications in approximation theory with emphasis
on computer applications", compiled by C.L. Lawson (Computer Reviews 2. (1968), 691-699). One may also consult the paper by Schultz and Varga
[67 - 34 J.
- 2 -
The journal abbreviations are those given in Mathematical Reviews
41 (1971), 1939-1960. We have strived to add to each paper one or more ref
ereaeea to reviews in Mathematical Reviews (MR), Zentralblatt fur Mathematik
(Zb), Computing Reviews (CR), Computer Abstracts (CA), Bulletin Signaletique
110 (BS) and DissertationJAbstracts (DA). An asterisk indicates that the
publication is a doctoral dissertation or a book that is mainly concerned
with spline functions.
The bibliography contains a total number of 368 items. The bulk of
these books and papers, 311 or 85%, has been published during the years
1966-1970. This clearly shows the explosive growth of this part of approxi
mation theory. Although the bibliography is certainly not complete, we hope
that it gives a reasonable survey of the existing literature on spline func
tion theory until January I, 1971.
During the project Miss Yvonne Naus of the mathematics library of the
Technological University Eindhoven has been of valuable assistance to us. It
is a pleasure to thank her for all the work she has done.
- 3 -
Bibliography
1904
1. Runge, C.
Theorie und Praxis der Reihen. § 20.
Goschen'sche Verlagshandlung, Leipzig, 1904.
1938
1. Quade, W.; Collatz, L.
Zur Interpolationstheorie der reellen periodischen Funktionen.
S.-B. Preuss. Akad. Wiss. Phys.-Math. Kl. 30 (1938), 383-429.
(Zb ~' p. 397.)
1940
I. Favard, J.
Sur !'interpolation.
J. Math. Pures Appl. ~'no. 9 (1940), 281-306. (MR l' p. 114;
Zb 23, p. 24.)
1941
I. Popoviciu, T.
Notes sur les fonctions convexes d'ordre superieur. IX.
Bull. Math. Soc. Sci. Math. R.S. Roumanie 43 (1941), 85-141.
(MR ]_, p. 116.)
1942
I. Love, A.E.H.
A treatise on the mathematical theory of elasticity. § 262; p. !•04.
Dover, New York, 1944.
- 4 -
1946
1. Schoenberg. I.J.
Contributions to the problem of approximation of equidistant data by
analytic functions.
Part A: On the problem of smoothing of gradiation. A first class of
analytic approximation formulae.
Quart. Appl. Math. i (1946), 45-99. (MR l, p. 487.)
2. Schoenberg, I.J.
Contributions to the problem of approximation of equidistant data by
analytic functions.
Part B: On the problem of osculatory interpolation. A second class of
analytic approximation formulae.
Quart. Appl. Math. i (1946), 112-141. (MR ~' p. 55.)
1949
1. Sard, A.
Best approximate integration formulas; best approximation formulas. ~
Amer. J. Math. 2! (1949), 80-91. (MR lQ, p. 576; Zb 39. p. 341.)
2. Schoenberg, I.J.; Whitney, A.
Sur la positivite des determinants de translations des fonctions de
frequence de Polya, avec une application a un probleme d'interpolation.
C.R. Acad. Sci. Paris Ser. A 228 (1949), 1996-1998. (MR !l' p. 86.)
3. Synge, J.L.; Griffith, B.A.
Principles of mechanics. pp. 92-98.
McGraw-Hill, New York, 1949.
1950
1. Meyers, L.F.; Sard, A.
Best approximate integration formulas.
J. Math. and Phys. ~ (1950), 118-123. (MR ~- p. 83; Zb ~' p. 342.)
- 5 -
2. Meyers, L.F.; Sard, A.
Best interpolation formulas.
J. Math. and Phys. 29 (1950), 198-206. (MR ~' p. 396; Zb 40, p. 28.)
1953
1. Schoenberg, I.J.; Whitney, A.
1.
On Polya frequency functions. III: The positivity of translation deter
minants with an application to the interpolation problem by spline
curves.
Trans. Amer. Math. Soc. 74 (1953), 246-259. (MR .!!!_, p • 732.)
1956
Sokolnikoff, I.S.
Mathematical theory of elasticity. p. 1 •
McGraw-Hill, New York, 1956.
1957
1. Holladay, J.C.
A smoothest curve approximation.
Math. Tables Aids Comput. !l (1957), 233-243. (MR 20, 414;
Zb 84, p. 349.)
1958
1. Schoenberg, I.J.
Spline functions, convex curves and mechanical quadrature.
Bull. Amer. Math. Soc. 64 (1958), 352-357. (MR 20, 7174;
Zb 85, p. 337.)
- 6 -
1959
1. Golomb, M.; Weinberger, H.F.
Optimal approximation and error bounds.
On numerical approximation (Proc. Symp. Math. :Res. Center, Univ.
Wisconsin, April 1958. Ed. by R.E. Langer), pp. 117-190. Univ. of
Wisconsin Press, Madison, 1959. (MR ~' 12697; Zb 2!, p. 58.)
1960
I. Birkhoff, G.; Garabedian, H.L.
Smooth surface interpolation.
J. Math. and Phys. 39 (1960), 258-268. (MR 22, 10151; Zb ~' p. 129.)
2. Johnson, R.S.
On monosplines of least deviation.
Trans. Amer. Math. Soc. 96 (1960), 458-477. (~ 23, A270.)
3. Rutishauser, H.
Bemerkungen zur glatten Interpolation.
Z. Angew. Math. Phys. l! (1960), 508-513. (MR ~' 883.)
4. Schwerdtfeger, H.
Notes on numerical analysis. II: Interpolation and curve fitting by
sectionally linear functions.
Canad. Math. Bull. l (1960), 41-57. (Zb 96, p. 103.)
1961
I. Schwerdtfeger, H.
Notes on numerical analysis. III: Further remarks on sectionally linear
functions.
Canad. Math. Bull. i (1961), 53-55. (Zb 106, p. 109.)
2. Theilheimer, F.; Starkweather, W.
The fairing of ship lines on a high-speed computer.
Math. Comp. ~ (1961), 338-355. ~ ~' B1627; Zb 109, p. 350.)
- 7 -
3. Weinberger, H.F.
Optimal approximation for functions prescribed at equally spaced
points.
1961/62
J. Res. Nat. Bur. Standards Sect. B 65 (1961), 99-104. (MR 25, 3616;
Zb 168, p. 149.)
1962
I. Asker, B.
The spline curve, a smooth interpolating function used in numerical
design of ship-lines.
BIT~ (1962), 76-82. (Zb ~' p. 81.)
2. Boor, C. de
Bicubic spline interpolation.
J. Math. and Phys. ~ (1962), 2I2-218. (MR 28, 1735; Zb 108, p. 271.)
3. Landis, F.; Nilson, E.N.
The determination of thermodynamic properties by direct differentia
tion techniques.
Progress in international research on thermodynamic and transport prop
erties (Second Symp. on Thermophysical Properties. Ed. by J.F. Masi and
D.H. Tsai), pp. 218-227. Acad. Press, New York, 1962.
4. Petersen, I.
On a piecewise polynomial approximation (Russian; Estonian and German
summaries).
Eesti NSV Tead. Akad. Toimetised Fuus.-Mat. II (1962), 24-32.
(MR 25, 3307.)
5. Walsh, J.L.; Ahlberg, J.H.; Nilson, E.N.
Best approximation properties of the spline fit.
J. Math. Mech. ll (I962), 225-234. (MR 25, 738; Zb I96, p. 486.)
- 8 -
I963
I. Ahlberg, J.H.; Nilson, E.N.
Convergence properties of the spline fit.
J. Soc. Indust. Appl. Math. ll (I963), 95-I04. (MR 27, 2763;
Zb 196, p. 487.)
2. Boor, C. de
Best approximation properties of spline functions of odd degree,
J. Math. Mech. 12 (1963), 747-749. (MR 27, 3982; Zb ~' p. 276.)
3. Sard, A.
Linear approximation.
1963/64
American Mathematical Society, Providence, R.I., 1963. (MR 28, 1429;
Zb J..!1, p • 54 • )
4. Schaefer, H.
Latteninterpolation bei einer Funktion von zwei Veranderlichen.
Z. Angew. Math. Phys. Ji (1963), 90-96. (Zb 108, p. 300.)
1964
I. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
Fundamental properties of generalized splines.
Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1412-I419. (MR 36, 6846;
Zb ]~, p. 362.)
2. Birkhoff, G.; Boor, C. de
Error bounds for spline interpolation.
J. Math. Mech. ll (1964), 827-835. (MR ~' 2583; Zb 144, p. 285.)
3. Collatz, L.
Einschliessungssatz fur die Minimalabweichung bei der Segmentapproxima
tion.
Simposio internazionale sulle applicazioni dell' Analisi alla Fisica
Matematica (Cagliari-Sassari, 1964), pp. I1-21. Cremonese, Rome, 1965.
(MR35, 633.)
- 9 -
4. Ferguson, J.
Multivariable curve interpolation.
J. Assoc. Comput. Mach. ll (1964), 221-228. (MR 28, 5551;
Zb 123, p. 330; CA ~, 1806.)
5. Greville, T.N.E.
Numerical procedures for interpolation by spline functions.
1964
SIAM J. Numer. Anal. l (1964), 53-68. (MR 36, 4784; Zb l!L, p. 336.)
6. Mehlum, E.
A curve-fitting method based on a variational criterion.
BIT~ (1964), 213-223. (MR 30, 4376.)
7. Schoenberg, I.J.
Spline interpolation and best quadrature formulae.
Bull. Amer. Math. Soc. 70 {1964), 143-148. (MR 28, 394; Zb 136, p. 362.)
8. Schoenberg, I.J.
Spline interpolation and the higher derivatives.
Proc. Nat. Acad. Sci. U.S.A.~ {1964), 24-28. (MR ~' 3278;
Zb 136, p. 362.)
9. Schoenberg, I.J.
On best approximations of linear operators.
Nederl. Akad. Wetensch. Proc. Ser. A 67 {1964), 155-163. (MR 28, 4284;
Zb 146, p. 85.)
10. Schoenberg, I.J.
On trigonometric spline interpolation.
J. Math. Mech. l1 (1964), 795-825. (MR ~' 2589; Zb 147, p. 321.)
II. Schoenberg, I.J.
Spline functions and the problem of graduation.
Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 947-950. {MR 29, 5040;
Zb 147, p. 321.)
12. Schoenberg, I.J.
On interpolation by spline functions and its minimal properties.
On approximation theory {Proc. Con£. Oberwolfach, Aug. 1963. Ed. by
P.L. Butzer and J. Korevaar), pp. 109-129. Birkhauser Verlag, Basel,
1964. {MR ~' 5015; Zb 147, p.321.)
- 10 - 1965
1965
1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
Best approximation and convergence properties of higher-order spline
approximations.
J. Math. Mech. 14 (1965), 231-243. (MR 35, 5823; Zb ~' p. 68.)
2. Ahlberg, J.H., Nilson, E.N.; Walsh, J.L.
Convergence properties of generalized splines.
Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 344-350. (MR 36, 6847;
Zb 136, p. 363.)
3. Ahlberg, J.H.; Nilson, E.N.
Orthogonality properties of spline functions.
J. Math. Anal. Appl. l! (1965), 321-337. (MR 37, 660; Zb 136, p. 48.)
4. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
Extremal, orthogonality, and convergence properties of multidimensional
splines.
J. Math. Anal. Appl. l! (1965), 27-48. (MR li• 661; Zb 136, P• 48.)
5. Atteia, M.
GenEhalisation de la definition et des proprietes des "spline fonctions".
C.R. Acad. Sci. Paris Ser. A 260 (1965), 3550-3553. (MR 12.t 3340;
Zb 163, p. 377.)
6. Atteia, M.
nspline-fonctions" generalisees.
C. R. Acad. Sci. Paris Ser. A 261 (1965), 2149-2152. (MR 35, 3341.)
7. Birkhoff, G.; Boor, C.R. de
Piecewise polynomial interpolation and approximation.
Approximation of functions (Proc. Symp. on appr. functions, Gen. Motors
Res. Lab., Warren, Michigan, 1964. Ed. by H.L. Garabedian), pp. 164-190.
Elsevier, Amsterdam, 1965. (MR 32, 6646; Zb 136, p. 47.)
8. Schoenberg, I.J.
On monosplines of least deviation and best quadrature formulae.
SIAM J. Numer. Anal. ! (1965), 144-170. (MR 34, 2182; Zb 136, p. 362.)
- 11 - 1965/66
9. Secrest, D.
Numerical integration of arbitrarily spaced data and estimation of
errors.
SIAM J. Numer. Anal. £·(1965), 52-68. (MR 1!• :4176; Zb 135, p. 386.)
10. Secrest, D.
Best approximate integration formulas and best error bounds.
Math. Comp. I! (1965), 79-83. (MR 33, 1967; Zb 134, p. 136; CA ~' 831.)
11. Secrest, D.
Error bounds for interpolation and differentiation by the use of spline
functions.
SIAM J. Numer. Anal. ~·(1965), 440-447. (MR 33, 6231; Zb 144, p. 388.)
12. Wendroff, B.
Bounds for eigenvalues of some differential operators by the Rayleigh
Ritz method.
Math. Comp. 19 (1965), 218-224. (MR ll• 4169.)
1966
1. Ahlberg, J.H.; Nilson, E.N.
The approximation of linear functionals.
SIAM J. Numer. Anal. l (1966), 173-182. (MR 36, 589; Zb 147, p. 51.)
2. Atteia, M.
* Etude de certains noyaux et theorie des fonctions "spline" en Analyse
Numerique.
Universite de Grenoble. These. Grenoble, 1966.
3. Atteia, M.
Existence et determination des fonctions "spline" a plusieurs variables.
C.R. Acad. Sci. Paris Ser. A 262 (1966), 575...:·578. (MR 33, 3004;
Zb 168, p. 350.)
- 12 - 1966
4. Aubin, J.P.
* Approximation des espaces de distributions et des operateurs differen
tiels.
These Doct. Sci. Math. Paris, 1966. (BS ~' 16561.)
5. Barrodale, I.; Young, A.
A note on numerical procedures for approximation by spline functions.
Comput. J • .2_ (1966), 318-320. (MR 34, 2151; Zb 168, p. 149; CA.!.!_, 69.)
6. Birkhoff, G.; Boor, c. de; Swartz, B.; Wendroff, B.
Rayleigh-Ritz approximation by piecewise cubic polynomials.
SIAM J. Numer. Anal. l (1966), 188-203. (MR 34, 3773; Zb 144, p. 380;
CA ..!.Q., 3202.) y
7. Birman, M.S.; Solomjak, M.Z.
Approximation of the functions of the classes ~ by piecewise polynomip
al functions.
Dokl. Akad. Nauk SSSR lZ! (1966), 1015-1018 (Russian); translated as
Soviet Math. Dokl. L (1966), 1573-1577. (MR 35, 630.)
8. Boor, C. de
* The method of projections as applied to the numerical solution of two
point boundary value problems using cubic splines (doctoral disserta
tion).
University of Michigan, Ann Arbor, 1966. (BS 29, I 0097; DA '!:]_, 3592-B.)
9. Boor, C. de; Lynch, R.E.
On splines and their minimum properties.
J. Math. Mech. 11 (1966), 953-969. (MR 34, 3159; Zb 185, p. 205.)
I 0. Caras so, C.
* Methodes numeriques pour !'obtention de fonctions-spline.
Universite de Grenoble. These. Grenoble, 1966. (BS 28, 6538.)
II. Ciarlet, P.G.
* Variational methods for nonlinear boundary value problems (doctoral
dissertation).
Case Institute of Technology, Cleveland, 1966.
- 13 - 1966
12. Curry, H.B.; Schoenberg, I.J.
On folya frequency functions. IV: The fundamental spline functions and
their limits.
J. Analyse Math. ll (1966), 71-107. (MR ~' 1884; Zb 146, p. 84.)
13. Ehlich, H.
Untersuchungen zur numerischen Fourieranalyse.
Math. Z. 2l (1966), 380-420. (MR 34, 7057.)
14. Glass, J.M.
Smooth-curve interpolation: a generalized spline-fit procedure.
BIT~ (1966), 277-293. (Zb 173, p. 186; CR ~' 12801.)
15. Handscomb, D.C.
Spline functions.
Methods of numerical approximation. Ed. by D.C. Handscomb, pp. 163-167.
Pergamon Press, Oxfordt 1966.
16. Handscomb, D.C.
Optimal approximation by means of spline functions.
Methods of numerical approximation. Ed. by D.C. Handscomb, pp. 177-181.
Pergamon Press, Oxford, 1966.
17. Innanen, K.A.
An example of precise interpolation with a spline function.
J. Computational Phys. (1966), 303-304. (CR ~' 12789; CA ~' 71.)
18. Karlin, S.; Studden, W.J.
Tchebycheff systems: with applications in analysis and statistics.
pp. 140-143; pp. 436-454.
Interscience, New York, 1966. (MR 34, 4757; Zb 153, p. 389.)
19. Karlin, S.; Ziegler, Z.
Chebyshevian spline functions.
SIAM J. Numer. Anal. l (1966), 514-543. (MR 35, 7041; Zb !I!' p. 310.)
20. Malozemov, V.N.
On the deviation of broken lines (Russian, English summary).
Vestnik Leningrad. Univ. ~no. 7 (1966), 150-153. (MR 33, 4533;
Zb 177, p. 87.)
- 14 -
21. Marsden, M.; Schoenberg, I.J.
On variation diminishing spline approximation methods.
Mathematica (Cluj)!!' no, 31 (1966), 61-82. (MR 35, 4648;
Zb .!.2.!_, p • 3 I 0 • )
22. Milnes, H.W.
1966
A variational approach to smoothing unequally spaced data subject to
random errors.
Indust. Math. 16 (1966), 77-93. (MR 40, 5108.)
23. Schoenberg, I.J.
On Hermite-Birkhoff interpolation.
J. Math. Anal. Appl. ~ (1966), 538-543. (MR 34, 3160; Zb 156, p. 287.)
24. Schoenberg, I.J.
On monosplines of least square deviation and best quadrature formulae.
II.
SIAM J. Numer. Anal. l (1966), 321-328. (MR 34, 3170; Zb 147, p. 321.)
25. Schumaker, L.L.
* On some approximation problems involving Tchebycheff systems and spline
functions (doctoral dissertation).
Stanford University, Stanford, 1966. (BS 29, 2535; DA !L' 240-B.)
26. Schweikert, D.G.
* The spline in tension (hyperbolic spline) and the reduction of extrane
ous inflection points (doctoral dissertation).
Brown University, Providence, 1966. (DA 28, 267-B.)
27. Schweikert, D.G.
An interpolation curve using a spline in tension.
J. Math. and Phys. 45 (1966), 312-317. (MR 34, 6990; Zb 146, p. 141.)
28. Sharma, A.; Meir, A.
Degree of approximation of spline interpolation.
J. Math. Mech. ~ (1966), 759-767. (MR ~' 3006; Zb 158, p. 307.)
29. Stern, M.D.
* Some problems in the optimal approximation of bounded linear function
als (doctoral dissertation).
Oxford University, Oxford, 1966.
- IS - 1966/67
30. Varga, R. S.
Hermite interpolation-type Ritz methods for two-point boundary value
problems.
Numerical solution of partial differential equations (Proc. Symp. Univ.
Maryland, 1965. Ed. by J.H. Bramble), pp. 365-373. Acad. Press, New
York, 1966. (MR 34, 5302; Zb 1!!_, p. 357.)
1967
1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
Complex cubic splines.
Trans. Amer. Math. Soc. 129 (1967), 391-413. (MR 36, 573; BS 29, 11591.)
2. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
* The theory of splines and their applications.
Acad. Press, New York, 1967. (MR 39, 684; Zb 158, p. 159.)
3. Atteia, M.
Sur les fonctions-spline generalisees.
Actes du 5e Congres de l'AFIRO, Lille, 1966, PP• 113-116.
Assoc. Frany• d'Inform. et de Rech. Operat., Paris, 1967.
4. Atteia, M.
Fonctions "spline" avec contraintes lineaires de type inegalite.
Actes du 6e Congres de l'AFIRO, Nancy, 1967, pp. 42-54.
Assoc. Frany• d'Inform. et de Rech. Operat., Paris, 1967.
5. Aubin, J.P.
Approximation des espaces de distributions et des operateurs differen
tiels.
Bull. Soc. Math. France, supplement au numero de Decembre 1967.
Memoire no. 12. (BS 29, 9570.)
6. Aubin, J.P.
Behavior of the error of the approximate solutions of boundary value
problems for linear elliptic operators by Galerkin's and finite differ
ence methods.
Ann. Scuola Norm. Sup. Pisa ~ (1967), 599-637. (BS 29, 12060.)
- 16 - 1967
7. Birkhof£, G.
Local spline approximation by moments.
J. Math. Mech. li (1967), 987-990. (MR 34, 8051; Zb 148, p. 292.)
8. Birkhoff, G.; Priver, A.
Hermite interpolation errors for derivatives.
J. Math. and Phys. 46 (1967), 440-447. (MR 36, 1883; Zb 176, p. 142.)
9. Carasso, C.
Obtention d'une fonction-Spline d'interpolation d'ordre K par une
methode d'integration locale.
Procedures algol en analyse numerique, pp. 288-291.
Centre National de la Recherche Scientifique, Paris, 1967.
10. Carasso, C.
Methode pour l'obtention de fonctions-spline d'interpolation d'ordre
deux.
Procedures algol en analyse numerique, pp. 292-294.
Centre National de la Recherche Scientifique, Paris, 1967.
11. Carasso, C.
Obtention d'une fonction lisse passant par des points donnes et ayant
en ces points des derivees donnees (fonction-spline d'Hermite).
Procedures algol en analyse numerique, pp. 295-299.
Centre National de la Recherche Scientifique, Paris, 1967.
12. Carasso, G.
Obtention de la derivee d'une fonction donnee par points.
Procedures algol en analyse numerique, pp. 30Q-301.
Centre National de la Recherche Scientifique, Paris, 1967.
13. Carasso, C.
Construction numer~que de fonctions-spline.
Actes du 5e Congres de l'AFIRO, Lille, 1966, pp. 506-509.
Assoc. Fran)· d'Inform. et de Rech. Operat., Paris, 1967.
14. Carasso, C.
Methode generale de construction de fonctions spline.
Rev. Franyaise Informat. Recherche Operationelle l• no. 5 (1967),
119-127. (MR lZ_, 667; Zb 163, p. 377; BS 29, 13887.)
- 17 - 1967
15. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.
Numerical methods of high-order accuracy for nonlinear boundary value
problems. I: One dimensional problem.
Numer. Math. ~ (1967), 394-430. (MR 36, 4813; Zb 155, p. 204.)
16. Cybertowicz, Z.
On some approximation problems.
Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 11 (1967),
497-501. (Zb 176, p. 352.)
17. Ferrand, C,
Lissage par utilisation de fonctions analogues aux fonctions spline.
Actes du 6e Congres de l'AFIRO, Nancy, 1967, pp. 14-31.
Assoc. Franc. d'Inform. et de Rech. Operat., Paris, 1967.
18. Joly, J.L.
Spline functions, interpolation and numerical quadrature.
Mathematical methods for digital computers, Vol. II. Ed. by A. Ralston
and H.S. Wilf, pp. 156-168. Wiley, New York, 1967. (CR ~' 12020.)
19. Joly, J.L.
Utilisation des fonctions spline pour le lissage.
Actes du 5e Congres de l'AFIRO, Lille, 1966, pp. 349-352.
Assoc. Franc. d'Inform. et de Rech. Operat., Paris, 1967.
20. Joly, J.L.
Theoremes de convergence des fonctions spline generales d'interpola
tion et d'ajustement.
C.R. Acad. Sci. Paris Ser. A 264 (1967), 126-128. (MR 35, 3342;
Zb ]54, p. 149; BS 28, 9341.)
21. Karlin, S.; Schumaker, L.L.
The fundamental theorem of algebra for Tchebycheffian monosplines.
J. Analyse Math. 20 (1967), 233-270. (MR 36, 582; Zb 187, p. 20;
BS ~' 4264.)
- 18 - 1967
22. Karlin, S.; Ziegler, Z.
Chebyshevian spline functions.
Inequalities (Proc. Symp. Wright-Patterson Air Force Base, Ohio, 1965.
Ed. by 0. Shisha), pp. 137-149. Acad. Press, New York, 1967.
(MR ~' 1854; Zb ll!' p. 310.)
23. Loscalzo, F.R.; Talbot, T.D.
Spline function approximations for solutions of ordinary differential
equations.
Bull. Amer. Math. Soc. 2l (1967), 438-442. (MR 35, 1218;
Zb JI!, p. 363.)
24. Loscalzo, F.R.; Talbot, T.D.
Spline function approximations for solutions of ordinary differential
equations.
SIAM J. Numer. Anal.~ (1967), 433-445. (MR 36, 4808; Zb lZ!' p. 363;
CA ~' 90.)
25. Malozemov, V.N.
Polygonal interpolation.
Mat. Zametki l (1967), 537-540 (Russian); translated as Math. Notes
(1967), 355-357. (MR 35, 5816.)
26. Meinguet, J.
Optimal approximation and error bounds in seminormed spaces.
Numer. Math. 10 (1967), 370-380. (MR lr' 6012; CA ~' 878; BS 29, 4620.)
27. Munteanu, M.J.
Observations on optimal solutions of some nonlinear differential pro
blems with boundary values in the subspace of generalized spline func
tions (Roumanian).
Bul. Sti. Inst. Politehn. Cluj. lQ (1967), 47-56.
28. Nord, S.
Approximation properties of the spline fit.
BIT L (1967), 132-144. (MR 36, 1887; Zb lll' p. 373; CAll' 2215.)
- 19 - 1967
29. Perrin, F.M.
* An application of monotone operators to differential and partial dif
ferential equations on infinite domains (doctoral dissertation).
Case Institute of Technology, Cleveland, 1967.
30. Reinsch, C.H.
Smoothing by spline functions.
Numer. Math. 10 (1967), 177-183. (Zb l£l, p. 362; CR ~' 14528.)
31. Rice, J.R.
Characterization of Chebyshev approximations by splines.
SIAM J, Numer. Anal. i (1967), 557-565. (MR 36, 6851; Zb 187, p. 329.)
32. Sard, A.
Optimal approximation.
J. Functional Analysis
33. Schoenberg, I.J.
On spline functions.
(1967), 222-244. (MR 36, 3037; Zb 158, p. 136.)
Inequalities (Proc. Symp. Wright-Patterson Air Force Base, Ohio, 1965.
Ed. by 0. Shisha), pp. 255-291. Acad. Press, New York, 1967.
(MR 36, 6848.)
34. Schultz, M.H.; Varga, R.S.
1-splines.
Numer. Math. 10 (1967), 345-369. (MR 37, 665; Zb 183, p. 444; -- -- ---CA 12, 872.)
35. Stern, M.D.
Optimal quadrature formulae.
Comput. J. ~ (1967), 396-403. (MR 35, 3885; CA !l, 836.)
36. Subbotin, Yu.N.
Piecewise-polynomial (spline) interpolation.
Mat. Zametki 1 (1967), 63-70 (Russian); translated as Math. Notes
(1967), 41-45. (MR 35, 4645; Zb 159, p. 84.)
37. Young, J.D.
Numerical applications of cubic spline functions.
The Logistics Review~, no. 14 (1967), 9-14. (CR !l, 19816.)
- 20 - 1968
1968
1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
Cubic splines on the real line.
J. Approximation Theory l (1968), 5-10. (MR 37, 6650; Zb 179, p. 365.)
2. Amunrud, L.R.
* Tchebycheff approximations by general spline functions (doctoral dis
sertation).
Montana State University, Montana, 1968. (DA 29, 4254-B.)
3. Anselone, P.M.; Laurent, P.J.
A general method for the construction of interpolating or smoothing
spline-functions.
Numer. Math.~ (1968), 66-82. (MR 40, 3145; Zb 197, p. 135; CAll' 55.)
4. Atkinson, K.E.
On the order of convergence of natural cubic spline interpolation.
SIAM J. Numer. Anal.~ (1968), 89-101. (MR lit 1853; Zb 208, P• 408.)
5. Atteia, M.
Fonctions "spline" definies sur un ensemble convexe.
Numer. Math.~ (1968), 192-210. (MR iL' 2265; Zb 186, p. 452;
BS 30, 6605.)
6. Aubin, J.P.
Interpolation et approximation optimales et "spline functions".
J. Math. Anal. Appl. 24 (1968), 1-24. (MR lr' 6651.)
7. Aubin, J.P.
Best approximation of linear operators in Hilbert spaces.
SIAM J. Numer. Anal.~ (1968), 518-521. (MR 38, 6743; Zb 176, p. 131.)
8. Bickley, W.G.
Piecewise cubic interpolation and two-point boundary problems.
Comput. J. ll (1968), 206-208. (MR )7, 6036; Zb 155, p. 480;
CA ~' 2551; BS 30, 5010.)
- 21 - 1968
9. Birkhoff, G.; Schultz, M.H.; Varga, R.S.
Piecewise Hermite interpolation in one and two variables with applica
tions to partial differential equations.
Numer. Math. l! (1968), 232-256. (MR ll, 2404; Zb 159, p. 209;
CA g, 2291.)
10. Birkhoff, G.; Gordon, W.J.
The draftsman's and related equations.
J. Approximation Theory l (1968), 199-208. (MR 38, 4055.)
I 1 • Boor, C. de
On local spline approximation by moments.
J. Math. Mech. ll (1968), 729-735. (MR 36, 6850; Zb 162, p. 84.)
12. Boor, C. de
On the convergence of odd-degree spline interpolation.
J. Approximation Theory l (1968), 452-463. (MR 38, 6273; Zb 174, p. 99.)
13. Boor, C. de
On uniform approximation by splines.
J. Approximation Theory l (1968), 219-235. (MR 39, 1866; Zb 193, p. 25.)
14. Buchanan, J.E.; Thomas, D.H.
On least-squares fitting of two-dimensional data with a special struc
ture.
SIAM J. Numer. AnaL 1 (1968), 252-257. (MR ll, 3740.)
15. Bulirsch, R.; Rutishauser, H.
Spline-Interpolation.
Mathematische Hilfsmittel des Ingenieurs, Vol. III. Ed. by R. Sauer ancl.
I. Szabo, pp. 265-277. Springer, Berlin, 1968. (MR 37, 7115; - --Zb 193, p. 352.)
16. Cheney, E. W. ; Schurer, F.
A note on the operators arising in spline approximation.
J. Approximation Theory (1968), 94-102. (MR 37, 5580; Zb 177, p. 89.)
17. Cherruault, Y.
* Approximation d'operateurs lineaires et applications.
These, Paris, 1966.
Monographies d'Informatique, Vol. 4. Dunod, Paris, 1968. (MR 38, 4879;
Zb 169, p. I 96.)
- 22 -
18. Ciarlet, P.G.
An O(h2 ) method for a non-smooth boundary value problem.
Aequationes Math. l (1968), 39-49. (MR 38, 869; Zb 159, p. 117.)
19. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.
1968
Numerical methods of high-order accuracy for nonlinear boundary value
problems. II: Nonlinear boundary conditions.
Numer. Math, II (1968), 331-345. (MR lL' 4965; Zb ~' p. 149;
CA .!1_, 2548.)
20. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.
Numerical methods of high-order accuracy for nonlinear boundary value
problems. III: Eigenvalue problems.
Numer. Math. 12 (1968), 120-133. (MR 38, 1838; Zb ~' p. 183;
CA .!1_, 2 77. )
21. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.
Numerical methods of high-order accuracy for nonlinear boundary value
problems. IV: Periodic boundary conditions.
Numer. Math. g (1968), 266-279. (MR 39, 2337; Zb ~, p. 183.)
22. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.
Numerical methods of high-order accuracy for nonlinear two-point bound
ary value problems.
Programmation en Mathematiques Numeriques (Coll. Intern.CNRS,no. 165,
Besa~so~ 1966), pp. 217-225. Centre National de la Recherche Scienti
fique, Paris, 1968. (MR 38s 1837; Zb 207, p. 164.)
23. Cybertowicz, z. On some approximation problems.
Frace Mat. 12 (1968), 61-74. (MR 38, 2496.)
24. Diringer, P.
Interpolation, derivation et integration a l'aide de fonctions spline.
Recherche Aerospat. 124 (1968), 13-16. (BS 30, 5046.)
25. Einarsson, B.
Numerical calculation of Fourier integrals with cubic splines.
BIT 8 (1968), 279-286. (MR 39, 1114; Zb 187, p. 105; CA 13, 542.) ~ - -- --
- 23 -
26. Eltom, M.E.A.
* Numerical approximation of functions of one ore more variables
(doctoral dissertation).
Oxford University, Oxford, 1968.
27. Fix, G.
1968
* Bounds and approximations for eigenvalues of self-adjoint boundary
value problems (doctoral dissertation).
Harvard University, Cambridge (Mass.), 1968.
28. Golomb, M.
Approximation by periodic spline interpolants on uniform meshes.
J. Approximation Theory l (1968), 26-65. (MR 38, 1444; Zb 185, p. 309.)
29. Hall, C.A.
On error bounds for spline interpolation.
J. Approximation Theory l (1968), 209-218. (MR 39, 681; Zb 177, p. 89.)
30. Herbold, R.J.
* Consistent quadrature schemes for the numerical solution of boundary
value problems by variational techniques (doctoral dissertation).
Case Western Reserve University, Cleveland, 1968. (CR ~' 15006;
DA 30, 165-B.)
31. Hulme, B.L.
Interpolation by Ritz approximation.
J. Math. Mech. ~ (1968), 337-341. (MR lL• 7090; Zb 165, p. 386.)
32. Ikaunieks, E.A.; Ermu~a, A.E.
Concave piecewise-polynomial interpolation. (Russian; Latvian and
English summaries.)
Latvian Math. Yearbook, Vol. 4, pp. 149-163. Izdat. "Zinatne", Riga,
1968. (MR 39, 2293; Zb 208, p. 409.)
33. Jerome, J.W.; Schumaker, L.L.
A note on obtaining natural spline functions by the abstract approach
of Atteia and Laurent.
SIAM J. Numer. Anal. 5 (1968), 657-663. (MR 40, 6127; Zb 185, p. 409;
BS 30 , 14 544 . )
- 24 - 1968
34. Johnson, O.G.
* Convergence, error bounds, sensitivity, and numerical comparisons of
certain absolutely continuous Rayleigh-Ritz methods for Sturm-Liouville
eigenvalue problems (doctoral dissertation).
University of California, Berkeley, 1968. (DA ~. 3396-B.)
35. Karlin, S.
Total positivity, Vol. I. pp. 357-364; pp. 501-564.
Stanford Univ. Press, Stanford, California, 1968. (MR 37, 5667.)
36. Karlin, S.; Karon, J.M.
A variation-diminishing generalized spline approximation method.
J. Approximation Theory (1968), 255-268. (MR 38, 3664;
Zb 165, P• 386.)
37. Karon, J.M.
* The sign-regularity properties of a class of Green's functions for
ordinary differential equations and some related results (doctoral
dissertation).
Stanford Univ., Stanford, California, 1968. (DA ~' 2529-B.)
38. Laurent, P.J.
Representation de donnees experimentales a l'aide de fonctions-spline
d'ajustement et evaluation optimale de fonctionnelles lineaires conti-
nues.
Apl. Mat.~ (1968), 154-162. (MR 38, 4000; Zb 155, p. 219.)
39. Laurent, P.J.
Theoremes de characterisation en approximation convexe.
Mathema.tica (Cluj) .!.Q., no. 33 (1968), 95-111 •. (MR ±.!_, 701.)
40. Loscalzo, F.R.
* On the use of spline functions for the numerical solution of ordinary
differential equations (doctoral dissertation).
Univ. of Wisconsin, Madison, 1968. (DA 29, 2983-B.)
41. Marsden, M.J.
* An identity for spline functions with applications to variation-dimin
ishing spline approximation (doctoral dissertation).
Univ. of Wisconsin, Madison, 1968. (DA 29, 2985-B.)
- 25 -
42. Meir, A.; Sharma, A.
One-sided spline approximation.
Studia Sci. Math. Hungar. 1 (1968), 211-218. (MR 38, 1445;
Zb 175, p. 350.)
43. Meir, A.; Sharma, A.
Convergence of a class of interpolatory splines.
J. Approximation Theory l (1968), 243-250. (MR 38, 3665;
Zb 186, p. I 14. )
44. Phillips, G.M.
Algorithms for piecewise straight line approximations.
Comput. J. !l (1968), 211-212. OKR ~' 6013; Zb 165, p. 512;
CA _!!, 2529.)
45. Powell, M.J.D.
On best L2 spline approximations.
1968
Numerische Mathematik, Differentialgleichungen, Approximationstheorie
(Proc. Conf. Oberwolfach, 1966. Ed. by L. Collatz, G. Meinardus and
H. Unger), pp. 317-339. Birkhauser Verlag, Basel, 1968.
46. Sard, A.
Optimal approximation: an addendum.
J. Functional Analysis~ (1968), 368-369. (MR 38, 1457; Zb 159, p. 438.)
47. Schoenberg, I.J.
On the Ahlberg-Nilson extension of spline interpolation: the g-splines
and their optimal properties.
J. Math. Anal. Appl. 21 (1968), 207-231. (MR 36, 6849; Zb 159, p. 84.)
48. Schoenberg, I.J.
On spline interpolation at all integer points of the real axis.
Mathematica (Cluj) lQ, no. 33 (1968), 151-170. (MR 3~, 6274;
Zb 183, p. 331.)
49. Schoenberg, I.J.
Spline interpolation and the higher derivatives.
Abhandlungen aus Zahlentheorie und Analysis. Ed. by P. Turan, pp. 279-
295. Deutscher Verlag der Wissenschaften, Berlin, 1968. (Zb 198, p. 90.)
- 26 - 1968
50. Schumaker, L.L.
Uniform approximation by Tchebycheffian spline functions.
J. Math. Mech. ~ (1968), 369-377. (MR 39, 3203, Zb ~' p. 386.)
51. Schumaker, L.L.
Uniform approximation by Chebyshev spline functions. II: Free knots.
SIAM J. Numer. Anal. ~ (1968), 647-656. (MR 39, 3204; Zb 169, p. 394.)
52. Schurer, F.
A note on interpolating periodic quintic splines with equally spaced
nodes.
J. Approximation Theory! (1968), 493-500. (MR 38, 6275;
Zb 186, p. 114.)
53. Schurer, F.; Cheney, E.W.
On interpolating cubic splines with equally-spaced nodes.
Nederl. Akad. Wetensch. Proc. Ser. A 2! (1968), 517-524. (MR 40, 6129;
Zb 184, p. 379.)
54. Shisha, o. Trends in approximation theory.
Appl. Mech. Rev.~ (1968), 337-341. (BS 30, 2197.)
55. Simpson, R.B.
Approximation of the minimizing element for a class of functionals.
SIAM J. Numer. Anal. 5 (1968), 26-41. (MR lL' 3414; CA ~' 1956.)
56. Smirnov, V.M.
A certain method of smooth interpolation of functions.
Z. Vy~isl. Mat. i Mat. Fiz. ~ (1968), 1330-1331 (Russian); translated
as U.S.S.R. Comput. Math. and Math. Phys. ~~ no. 6 (1968), 190-193.
(MR ~' 5839.)
57. Spath, H.
Ein Verfahren zur flachentreuen Approximation von Treppenfunktionen
durch glatte Kurven.
Z. Angew. Math. Mech. 48 (1968), T106-T107. (BS 30, 18375.)
58. Studden, W.J.; Van Arman, D.J.
Admissible designs for polynomial spline regression.
Ann. Math. Statist. 40 (1968), 1557-1569. (MR 40, 2195.)
- 27 -
59. Swartz, B.
O(h2n+2-Q.) b d 1' . 1 . oun s on some sp 1ne 1nterpo at1on errors.
Bull. Amer. Math. Soc. 74 (1968), 1072-1078. (MR 38, 4869;
Zb .!.!!_, p. 340.)
60. Van Arman, D.J.
1968/69
* Classification of experimental designs relative to polynomial spline
regression functions (doctoral dissertation).
Purdue University, Lafayette, 1968. (DA 29, 3967-B.)
61. Young, J.D.
Numerical applications of hyperbolic spline functions.
The Logistics Review i• no. 19 (1968), 17-22. (CR !!' 19817.)
62. Young, J.D.
Numerical applications of damped cubic spline functions.
The Logistics Review i' no. 20 (1968), 33-37. (CR !l' 19818.)
1969
1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
Properties of analytic splines. I: Complex polynomial splines.
J. Math. Anal. Appl. 27 (1969), 262-278. (Zb 185, p. 135; BS 1!, 3145.)
2. Ahlberg, J.H.
Splines in the complex plane.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. i-27. Acad. Press, New York, 1969. (MR il' 2264.)
3. Albasiny, E.L.; Hoskins, W.D.
Cubic spline solutions to two-point boundary value problems.
Comput. J. ll (1969), 151-153. (MR 39, 3710; Zb 185, p. 414;
CA _!1, 3112.)
4. Amos, D.E.; Slater, M.L.
Polynomial and spline approximation by quadratic programming.
Comm. ACM ~ (1969), 379-381. (Zb 187, p. 127; CAll' 2422.)
- 28 - 1969
5. Barnhill, R.E.; Wixom, J.A.
An error analysis for the bivariate interpolation of analytic functions.
SIAM J. Numer. Anal.~ (1969), 450-457. (Zb 187, p. 501.)
6. Bellman, R.; Roth, R.
Curve fitting by segmented straight lines.
J. Amer. Statist. Assoc. 64 (1969), 1079-1084. (MR 39, 7760.)
7. Bickley, W.G.
Piecewise cubic interpolation and two-point boundary problems. (Letter
to the editor.)
Comput. J. 12 (1969), 105. (CA !l' 2789.)
8. Birkhoff, G.
Numerical solution of elliptic equations.
Lecture series in differential equations, vol. II. Ed. by A.K. Aziz,
pp. 197-232. Van Nostrand Reinhold Company, New York, 1969.
(Zb 208, p. 192.)
9. Birkhoff, G.
Piecewise bicubic interpolation and approximations in polygons.
Approximation with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 185-221. Acad. Press, New York, 1969.
10. Blue, J .L.
Spline function methods for nonlinear boundary-value problems.
Comm. ACM I! (1969), 327-330. (Zb 175, p. 161; CR lQ, 17706;
CA _!2, 2032.)
1 I . Boor, C. de
On the approximation by y-polynomials.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 157-183. Acad. Press, New York, 1969.
(MR ~' 4096.)
12. Carasso, C.; Laurent, P.J.
On the numerical construction and the practical use of interpolating
spline functions.
Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968. Ed. by
A.J.H. Morrell), Vol. I- Mathematics, Software, pp. 86-89.
North-Holland Publishing Company, Amsterdam, 1969. (MR 40, 8219;
Zbl2..!_, p. 449; CA~, 1477.)
- 29 - 1969
13. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.
Numerical methods of high-order accuracy for nonlinear boundary value
problems. V: Monotone operator theory.
Numer. Math. ll (1969), 51-77. (MR 40, 3730; Zb ~' p. 186;
CAll, 2420.)
14. Dailey, J.W.
* Approximation by spline-type functions and related problems (doctoral
dissertation).
Case Western Reserve University, Cleveland, 1969. (DA 1!, 3537-B.)
15. Elhay, S.
Optimal quadrature.
Bull. Austral. Math. Soc.! (1969), 81-108. (MR !!' 2925;
Zb 175, p. 351.)
16. Esch, R.E.; Eastman, W.L.
Computational methods for best spline function approximation.
J. Approximation Theory! (1969), 85-96. (MR 39, 1867; Zb ~' p. 176.)
17. Fitzgerald, C.H.; Schumaker, L.L.
A differential equation approach to interpolation at extremal points.
J. Analyse Math. 22 (1969), 117-134. (MR !!' 2257; BS 1!, 15430.)
18. Fix, G.
Higher-order Rayleigh-Ritz approximations.
J. Math. Mech. ~ (1969), 645-657. (MR 39, 2349.)
19. Fix, G.; Strang, G.
Fourier analysis of the finite element method in Ritz- Galerkin theory.
Studies in Appl. Math. 48 (1969), 265-273. (MR s..!_. 2944;
Zb 179, p. 225.)
20. Fyfe, D.J.
The use of cubic splines in the solution of two-point boundary value
problems.
Comput. J. l! (1969), 188-192. Q{R 39, 5065; Zb 185, p. 414;
CA ll' 3137.)
- 30 - 1969
21. Golomb, M.
Spline interpolation near discontinuities.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 51-74. Acad. Press, New York, 1969. (MR il, 693.)
22. Gordon, W.J.
Distributive lattices and the approximation of multivariate functions.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 223-277. Acad. Press, New York, 1969.
23. Gordon, W.J.
Spline-blended surface interpolation through curve networks.
J. Math. Mech. 18 (1969), 931-952. (MR 39, 7333; Zb 192, p. 422;
BS 30, 803.)
24. Greville, T.N.E.
* Theory and applications of spline functions.
Proc. Seminar Math. Res. Center, Univ. Wisconsin, Oct. 1968. Ed. by
T.N.E. Greville.
Acad. Press, New York, 1969. (MR 38, 3663.)
25. Greville, T.N.E.
Introduction to spline functions.
Theory and applications of spline functions (Proc. Seminar Math. Res.
Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 1-35.
Acad. Press, New York, 1969. (MR 39, 1868.)
26. Hall, C.A.
Error bounds for periodic quintic splines.
Comm. ACM ~ (1969), 450-452. (Zb 185, p. 408; CR !l' 18293;
CA ~, 2778.)
27. Hall, C.A.
Bicubic interpolation over triangles.
J. Math. Mech. ~ (1969), 1-11. (MR 39, 6523; Zb 194, p. 471.)
- 31 - 1969
28. Heindl, G.
Spline-Funktionen meh~erer Verinderlicher. I: Definition und Erzeugung
durch Integration.
Bayer. Akad. Wiss. Math.-Natur. Kl. S.-B. (1969), 49-63. (BS 32, 5690.)
29. Herbold, R.J.; Schultz, M.H.; Varga, R.S.
The effect of quadrature errors in the numerical solution of boundary
value problems by variational techniques.
Aequationes Math. l (1969), 247-270. Of[ !!• 6410; Zb 196, p. 176.)
30. Hilbert, S.R.
* Numerical methods for elliptic boundary problems (doctoral disserta
tion).
University of Maryland, College Park, 1969. (DA lL• 1399-B.)
31. Hill, I.D.
Note on algorithm 40: Spline interpolation of degree three.
Comput. J. ~ (1969), 409.
32. Hulme, B.L.
* Piecewise bicubic methods for plate bending problems (doctoral disser
tation).
Harvard University, Cambridge (Mass.), 1969.
33. Jerome, J.W.; Varga, R.S.
Generalizations of spline functions and applications to nonlinear
boundary value and eigenvalue problem..
Theory and applications of spline functions (Proc. Seminar Math. Res.
Ceriter, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 103-
155. Acad. Press, New York, 1969. (MR 39, b85; Zb 188, p. 130.)
34. Jerome, J.W.; Schumaker, L.L.
On Lg-splines.
J. Approximation Theory! (1969), 29-49. (MR 39, 3201; Zb 172, p. 345.)
35. Jerome, J.W.; Schumaker, L.L.
Characterizations of functions with higher order derivatives in L • p
Trans. Amer. Math. Soc. 143 (1969), 36l-l71. (Zb 187, p. 377.)
- 32 - 1969
36. Johnson, O.G.
Error bounds for Sturm-Liouville eigenvalue approximations by several
piecewise cubic Rayleigh-Ritz methods.
SIAM J. Numer. Anal. 6 (1969), 317-333. (MR !l• 4789; Zb 183, p. 446.)
37. Karlin, S.
Best quadrature formulas and interpolation by splines satisfying bound
ary conditions.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 447-466. Acad. Press, New York, 1969.
(MR !it 2275.)
38. Karlin, S.
The fundamental theorem of algebra for monosplines satisfying certain
boundary conditions and applications to optimal quadrature formulas.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 467-484. Acad. Press, New York, 1969.
(MR !it 2276.)
39. Karon, J .M.
The sign-regularity properties of a class of Green's functions for
ordinary differential equations.
J. Differential Equations~ (1969), 484-502. (MR iL• 3863.)
~~ y r 39a. Korne1cuk, N.P.; Luspa1, N.E.
Best quadrature formulas for classes of differentiable functions and
piecewise-polynomial approximation.
Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 1416-1437 (Russian); trans
lated as Math. USSR·-Izv. l (1 969), 1335- J 355. (Zb 198, p. 89.)
40. Krinzesza, F.
* Zur periodischen Spline-Interpolation (doctoral dissertation).
Ruhr-Universitat, Bochum, 1969.
41. Lathrop, J.F.
* Application of spline functions to the numerical solution of ordinary
and partial differential equations (doctoral dissertation).
University of Colorado, Boulder, 1969. (DA 30, 4701-B.)
42. Laurent, P.J.
Construction of spline functions in a convex set.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 415-446. Acad. Press, New York, 1969.
(MR 40, 6147.)
- 33 - 1969
43. Lee, J.W.
* The study of a class of boundary value problems with cyclic totally
positive Green's functions with applications to spline approximation
and eigenvalue problems (doctoral dissertation).
Stanford University, Stanford, California, 1969. (DA 1Q, 1244-B.)
44. Loginov, A.S.
Approximation of continuous functions by broken lines.
Mat. Zametki ~ (1969), 149-160 (Russian); translated as Math. Notes 6
(1969), 549-555. (MR ~' 687; Zb 177, p. 88.)
45. Loscalzo, F.R.
An introduction to the application of spline functions to initial value
problems.
Theory and applications of spline functions (Proc. Seminar Math. Res.
Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 37-64.
Acad. Press, New York, 1969. (MR 39, 2334; Zb 12!' p. 165.)
46. Mangasarian, O.L.; Schumaker, L.L.
Splines via optimal control.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 119-156. Acad. Press, New York, 1969.
(MR ~, 4073.)
47. Mansfield, L.E.
* Optimal approximation and error bounds 1n spaces of multivariate func
tions (doctoral dissertation).
University of Utah, Salt Lake City, 1969. (DA 30, 2298-B.)
48. Meir, A.; Sharma, A.
On uniform approximation by cubic splines.
J. Approximation Theory! (1969), 270-274. (MR 40, 3137;
Zb 183, p. 330.)
49. Morin, M.
* Methodes de calcul des fonctions "spline" dans un ·convexe.
Universite de Grenoble. These. Grenoble, 1969. (BS ll' 17640.)
- 34 - 1969
50. Murty, V.N.
* Optimal designs of individual regression coefficients with a
Tchebycbeffian spline regression function (doctoral dissertation).
Purdue University, Lafayette, 1969. (DA 30, 5283-B.)
51. Natterer, F.
Numerische Behandlung singularer Sturm-Liouville-Probleme.
Numer. Math. 11 (1969), 434-447. (MR 40, 5143; Zb 182, p. 497.)
52. Nitsche, J.
Satze vom Jackson-Bernstein-Typ fur die Approximation mit Spline
Funktionen.
Math. z. 109 (1969), 97-106. (MR 39, 4567; Zb 174, p. 355.)
53. Nitsche, J.
Orthogonalreihenentwicklung nach linearen Spline-Funktionen.
J. Approximation Theory! (1969), 66-78. (MR 40, 4653; Zb 174, p. 360.)
54. Nitsche, J.
Umkehrsatze fur Spline-Approximationen.
CompositioMath.~ (1969), 400-416. (MR ~, 4074; Zb 199, p. 393.)
55. Nitsche, J.
Eine Bemerkung zur kubischen Spline-Interpolation.
Abstract spaces and approximation (Proc. Con£. Oberwolfach, 1968.
Ed. by P.L. Butzer and B.S. Nagy), pp. 367-372. Birkhauser Verlag,
Basel, 1969. (MR ~~ 7344; Zb 202, P• 158; BS 11, 9425.)
56. Nitsche, J.
Verfahren von Ritz und Spline-Interpolation bei Sturm-Liouville
Randwertproblemen.
Numer. Math. ll (1969), 260-265. (Zb j!!, p. 182; CR !l' 18291.)
57. Perrin, F.M.; Price, H.S.; Varga, R.S.
On higher-order numerical methods for nonlinear two-point boundary
value problems.
Numer. Math. 13 (1969), 180-198. (MR 40, 8276; Zb 183, p. 445.)
- 35 - 1969
58. Pierce, J.G.
* Higher order convergence results for the Rayleigh-Ritz method applied
to a special class of eigenvalue problems (doctoral dissertation).
Case Western Reserve University, Cleveland, 1969.(DA 30, 4264-B.)
59. Powell, M.J.D.
A comparison of spline approximations with classical interpolation
methods.
Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968. Ed. by
A.J.H. Morrell), Vol. I -Mathematics, Software, pp. 95-98.
North-Holland Publishing Company, Amsterdam, 1969. (MR 40, 8223;
Zb 194, p. 4 71; CA ~' 146 7.)
60. Powell, M.J.D.
The local dependence of least squares cubic splines.
SIAM J. Numer. Anal.~ (1969), 398-413. (MR il' 1192; Zb 183, p. 441.)
61 • Rice, J. R.
The approximation of functions. Vol. II: Nonlinear and multivariate
theory. pp. 123-167.
Addison-Wesley, Reading, 1969. (MR 39, 5989; Zb 185, p. 306.)
62. Rice, J.R.
On the degree of convergence of nonlinear spline approximation.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 349-365. Acad. Press, New York, 1969.
(MR 42, 2226.)
63. Ritter, K.
Generalized spline interpolation and nonlinear programming.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 75-117. Acad. Press, New York, 1969.
64. Ritter, K.
Two dimensional splines and their extremal properties.
Z. Angew. Math. Mech. 49 (1969), 597-608. (MR 40, 6128; Zb 194, p. 95.)
- 36 -
65. Rivlin, T.J.
An introduction to the approximation of functions. pp. 104-119.
Blaisdell P.C., Waltham, 1969. (MR 40, 3126; Zb 189, p. 66.)
66. Sakai, M.
Error estimation on piecewise Hermite interpolation.
1969
Mem. Fac. Sci. Kyushu Univ. Ser. A 23 (1969), 71-78. (Zb 201, p. 77.)
67. Schaback, R.
* Spezielle rationale Splinefunktionen (doctoral dissertation).
Universitat Munster, 1969.
68. Schoenberg, I.J.
Monosplines and quadrature formulae.
Theory and applications of spline functions (Proc. Seminar Math. Res.
Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 157-
207. Acad. Press, New York, 1969. (MR 39, 3202; Zb 203, p. 370.)
69. Schoenberg, I.J.
* Approximations with special emphasis on spline functions.
Proc. Symp. Math. Res. Center, Univ. Wisconsin, May 1969. Ed. by
I. J. Schoenberg.
Acad. Press, NewYork,·1969. (MR40, 4638.)
70. Schoenberg, I.J.
Cardinal interpolation and spline functions.
J. Approximation Theory~ (1969), 167-206. (MR ~~ 2266;
Zb 202, p. 348.)
71. Schoenberg, I.J.
Spline interpolation and the higher derivatives.
Number theory and analysis (papers in honor of Edmund Landau),
pp. 279-295. Plenum, New York, 1969. (MR il' 5848.)
72. Schultz, M.H.
Multivariate spline functions and elliptic problems.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 279-347. Acad. Press, New York, 1969.
(MR !!..!_, 221 0. )
- 37 -
73. Schultz, M.H.
Multivariate L-spline interpolation.
J. Approximation Theory~ (1969), 127-135. (MR 40, 3138;
Zb 202, p. 349.)
74. Schultz, M.H.
100
-multivariate approximation theory.
1969
SIAM J. Numer. Anal. ~ (1969), 161-183. (MR 40, 4639a; Zb 202, p. 159;
CA ~' 76.)
75. Schultz, M.H.
1 2-multivariate approximation theory.
SIAM J. Numer. Anal. ~ (1969), 184-209. (MR 40, 4639b; Zb 202, p. 159;
CA ~' 77.)
76. Schultz, M.H.
L2-approximation theory of even order multivariate splines.
SIAM J. Numer. Anal..£_ (1969), 467-475. (MR i!._, 1193; Zb 198, p. 400.)
77. Schultz, M.H.
Rayleigh-Ritz-Galerkin methods for multidimensional problems.
SIAM J. Numer. Anal • .£_ (1969), 523-538. (MR i!._, 7859; Zb ~' p. 193;
CR 1!, 20346; CA ~' 1193.)
78. Schultz, M.H.
Approximation theory of multivariate spline functions in Sobolev
spaces.
SIAM J. Numer. Anal • .£_ (1969), 570-582. (MR i~' 7823; Zb ~' p. 188;
CA ~' I 179.)
79. Schultz, M.H.
The Galerkin method for nonselfadjoint differential equations.
J. Math. Anal. Appl. 28 (1969), 647-651. (Zb 197, p. 137.)
80. Schumaker, 1.1.
Approximation by splines.
Theory and applications of spline functions (Proc. Seminar Math. Res.
Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 65-85.
Acad. Press, New York, 1969. (MR 39, 686; Zb 187, p. 328.)
- 38 - 1969
81. Schumaker, L.L.
Some algorithms for the computation of interpolating and approximating
spline functions.
Theory and applications of spline functions (Proc. Seminar Math. Res.
Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 87-102.
Acad. Press, New York, 1969. (MR 39, 687; Zb 188, p. 223.)
82. Schumaker, L.L.
On the smoothness of best spline approximations.
J. Approximation Theory~ (1969), 410-418. (MR il' 4076; Zb 183, p. 59.)
83. Sharma, A.; Meir, A.
Convergence of a class of interpolatory splines.
Abstract spaces and approximation (Proc. Conf. Oberwolfach, 1968.
Ed. by P.L. Butzer and B.S. Nagy), pp. 373-374·. Birkhauser Verlag,
Basel, 1969. (Zb 187, p. 329.)
84. Sims, S.E.
* Convergence properties of spline functions (doctoral dissertation).
University of Arizona, Tucson, 1969. (DA 30, 3763-B.)
85. Sonneveld, P.
Errors in cubic spline interpolation.
J. Engrg. Math. 1_ (1969), 107-117. (MR 40, 601; Zb 183, P• 442.)
86. Spath, H.
Algorithmus 10: Zweidimensionale glatte Interpolation; Twodimensional
smooth interpolation.
Computing (Arch. Elektron. Rechnen) 4 (1969), 178-182. (CA !l' 2431;
BS l.!_, 3141 • )
87. Spath, H.
Exponential spline interpolation.
Computing (Arch. Elektron. Rechnen) ~ (1969), 225-233. (MR 40, 2216;
Zb 184, p. 198; CR l!' 18512; CA 11, 3156; BS 30, 8074.)
88. Spath, H.
Algorithm 40: Spline interpolation of degree three.
Comput. J. 12 (1969), 198-199. (CA !l' 3144b.)
- 39 - / f
89. Spath, H.
Algorithm 42: Interpolation by certain quintic splines.
Comput. J. 12 (1969), 292-293. (CA ~' 356b.)
90. Spath, H.
1969
* Die numerische Berechnung von interpolierenden Spline-Funktionen mit
Blockunterrelaxation (doctoral dissertation).'
Universitat Karlsruhe, 1969.
91. Stephens, A.B.
* Convergence of the residual for Ritz-Galerkin approximation (doctoral
dissertation).
University of Maryland, College Park, 1969. (DA ll' 296-B.)
92. Storchai, V.F.
The deviation of polygonal functions in the L metric. p
Mat. Zametki 5 (1969), 31-37 (Russian); translated as Math. Notes 5
(1969), 21-25. (MR 39, 688; Zb 177, p. 88.)
93. Swartz, B.; Wendroff, B.
Generalized finite-difference schemes.
Math. Comp. 23 (1969), 37-49. (MR 39, 1125; Zb 184, p. 385.)
94. Tihomirov, V.M.
Best methods of approximation and interpolation of differentiable func
tions in the space C[-1,1].
Mat. Sb. 80, no. 122 (1969), 290-304 (Russian); translated as Math.
USSR-·Sb. 2_ (1969), 275-289. (MR 41, 703; Zb 204, p. 133.)
95. Varga, R.S.
Error bounds for spline interpolation.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 367-388. Acad. Press, New York, 1969.
(MR 40, 6130.)
96. Wakoff, G.I.
* Piecewise polynomial spaces and their use with the Rayleigh-Ritz
Galerkin method (doctoral dissertation).
Harvard University, Cambridge (Mass.), 1969.
- 40 -
97. Wendroff, B.
First principles of numerical analysis. pp. 62-67.
Addison-Wesley, Reading, 1969. (Zb 194, p. 178; BS 30, 18456.)
98. Woodford, C.H.
Smooth curve interpolation.
BIT~ (1969), 69-77. (CR lQ, 18077.)
99. Young, J.D.
Generalization of segmented spline fitting of third order.
The Logistics Review 1, no. 23 (1969), 33-40. (CR ll, 19819.)
100. Ziegler, z. One-sided L1-approximation by splines of an arbitrary degree.
Approximations with special emphasis on spline functions. Ed. by
I.J. Schoenberg, pp. 405-413. Acad. Press, New York, 1969.
(MR40, 7684.)
1970
I. Ahlberg, J.H.
Spline approximation and computer-aided design.
Advances in Computers, Vol. 10. Ed. by F.L. Alt and M. Rubino££,
pp. 275-289. Acad. Press, New York, 1970. (BS 32, 5046.)
2. Ahlberg, J.H; Nilson, E.N.
Polynomial splines on the real line.
J. Approximation Theory l (1970), 398-409.
2a. Akima, H.
1969/70
A new method of interpolation and smooth curve fitting based on local
procedures.
J. Assoc. Comput. Mach. 17 (1970), 589-602. (Zb 209, p. 468.)
3. Atteia, M.
Fonctions "Spline" et noyaux reproduisants d'Aronszajn-Bergman.
Rev. Fran~aise Informat. Recherche Operationnelle ~ (1970), 31-43.
(BS 32, 4653.)
4. Barrar, R.B.; Loeb, H.L.
Existence of best spline approximations with free knots.
J. Math. Anal. Appl. l! (1970), 383-390. (MR ~' 8887; Zb 194, p. 368.)
- 41 - 1970
5. Birkhoff, G.; Fix, G.
Accurate eigenvalue computations for elliptic problems.
Numerical solution of field problems in continuum physics (SIAM-AMS
Proc.), vol. II, pp.Ill-151. Amer. Math. Soc., Providence, R.I., 1970.
(MR i!_, 4827.)
6. Bramble, J.H.; Hilbert, S.R.
Estimation of linear functionals on Sobolev spaces with application to
Fourier transforms and spline interpolation.
SIAM J. Numer. Anal. l (1970), 112-124. (MR i!_, 7819; Zb 201, p. 78;
CR ~' 19963; CAli' 2086.)
7. Bramble, J.H.; Schatz, A.H.
Rayleigh-Ritz-Galerkin methods for Dirichlet's problem using subspaces
without boundary conditions.
Comm. Pure Appl. Math. 23 (1970), 653-675. (MR 42, 2690;
Zb 195, p. 388.)
8. Cavaretta, A.S. jr.
* On cardinal perfect splines of least sup norm on the real axis (doctoral
dissertation).
University of Wisconsin, Madison, 1970. (DA ll' 674G-B.)
9. Chan, P.P.-Y.
* Approximation theory with emphasis on spline functions and applications
to differential and integral equations (doctoral dissertation).
Case Western Reserve University, Cleveland, 1970. (DA l!_, 4191-B.)
10. Cheney, E.W.; Schurer, F.
Convergence of cubic spline interpolants.
J. Approximation Theory 2 (1970), 114-116. (MR 40, 7680;
Zb 193, p. 25; BS 30, 12879.)
II. Cheney, E.W.; Price, K.H.
Minimal projections.
Approximation theory (Proc. Symp., Lancaster, July 1969. Ed. by
A. Talbot), pp. 261-289. Acad. Press, London, 1970. (MR 42, 751.)
- 42 - 1970
12. Chi, D. N.-H.
* Linear multistep methods based on g-splines, (doctoral dissertation).
University of Pittsburgh, 1970. (DA 1!• 2812-B.)
13. Chu, S.C.
Piecewise polynomials and the partition method for nonlinear ordinary
differential equations.
J. Engrg. Math. ! (1970), 65-76. (MR il' 2933; Zb 208, P• 418.)
14. Ciarlet, P.G.; Varga, R.S.
Discrete variational Green's function. II: One dimensional problem.
Numer. Math. J! (1970), 115-128. (CA 11, 825; BS 32, 1231.)
15. Covaci-Munteanu, M.J.
* Contributions a la theorie des fonctions splines a une et a plusieurs
variables.
Universite Catholique de Louvain. These. Louvain, 1970.
16. Curtis, A.R.
The approximation of a function of one variable by cubic splines.
Numerical approximation to functions and data. Ed. by J.G. Hayes,
pp. 28-42. Athlone Press, London, 1970. (CR ~' 20155.)
17. Douglas, J. jr.; Dupont, T.
Galerkin methods for parabolic equations.
SIAM J. Numer. Anal. l (1970), 575-626.
18. Freud, G.; Popov, V.A.
Some questions that are related to the approximation by spline func
tions and polynomials.
Studia Sci. Math. Hungar. 5 (1970), 161-171 (Russian). (MR 42, 2225;
Zb 201, p. 396.)
19. Fyfe, D.J.
The use of cubic splines in the solution of certain fourth order
boundary value problems.
Comput. J. 11 (1970), 204-205. (MR il' 6407; Zb 191, p. 167;
CA_!i, 2110.)
- 43 - 1970
20. Gaier, D.
Saturation bei Spline-Approximation und Quadratur.
Numer. Math. 16 (1970), 129-140. (Zb 188, p. 223; BS ll• 1202.)
21. Galkin, P.V.
The possibility of periodic spline interpolation.
Mat. Zametki ~ (1970), 563-574 (Russian); translated as Math. Notes 8
(1970), 786-791.
22. Gold, S.C.
* Data smoothing using least-square spline functions (doctoral disserta
tion).
University of Utah, Salt Lake City, 1970. (DA ll' 4684-B.)
23. Greville, T.N.E.
Table for third-degree spline interpolation with equally spaced argu
ments.
Math. Comp. 24 (1970), 179-183. (MR ~' 2885; Zb 194, p. 471.)
24. Handscomb, D.C.
Characterization of best spline approximations with free knots.
Approximation theory (Proc. Symp., Lancaster, July 1969. Ed. by
A. Talbot), pp. 63-70. Acad. Press, London, 1970.
(MR 42, 735.)
25. Hayes, J.G.
Numerical approximation to functions and data.
Proc. Conf. Inst. Math. Appl., Canterbury, 1967. Ed. by J.G. Hayes.
Athlone Press, London, 1970. (CR ll• 19948.)
26. Hertling, J.
Approximation of piecewise continuous functions by a modification of
piecewise Hermite interpolation.
Numer. Math. 15 (1970), 404-414. (MR 42, 2223; Zb 194, p. 185;
CA li• 3286.)
- 44 -
27. Hoskins, W.D.
Algorithm 62: Interpolating quintic splines on equidistant knots.
Comput. J. 13 (1970), 437-438. (CA 11, 330j.)
28. Hung, H.-s.
1970
* The numerical solution of differential and integral equations by spline
functions (doctoral dissertation).
University of Wisconsin, Madison, 1970.
29. Ionescu, D.V.
Introduction a la theorie des "fonctions spline".
Acta Math. Acad. Sci. Hungar. ~ (1970), 21-26. (Zb 206, p. 348.)
30. Janenko, N.N.; Kvasov, B.I.
An iterative method for the construction of polycubic spline functions.
Dokl. Akad. Nauk SSSR 195 (1970), 1055-1057 (Russian); translated as
Soviet Math. Dokl. II (1970), 1643-1645. (BS 32, 3471.)
31. Jerome, J.W.
Linear self-adjoint multipoint boundary value problems and related
approximation schemes.
Numer. Math. 15 (1970), 433-449. (CAli' 3296.)
32. Kalik, c. Une propriete de minimum des fonctions "spline".
Studia Univ. Babe~-Bolyai Ser. Math.-Mech. ~ (1970), 35-46.
(MR i!' 8889; BS ll' 20299.)
33. Karlin, S.; Karon, J.
A remark on B-splines.
J. Approximation Theory l (1970), 455.
34. Karlin, S.; Lee, J.
Periodic boundary-value problems with cyclic totally positive Green's
functions with applications to periodic spline theory.
J. Differential Equations~ (1970), 374-396. (Zb 203, p. 103.)
35. Kautsky, J.
Optimal quadrature formulae and minimal monosplines in L • q
J. Austral. Math. Soc. II (1970), 48-56. (MR i!' 2277; Zb 187, p. 20.)
- 45 - 1970
36. Kimeldorf, G.S.; Wahba, G.
A correspondence between Bayesian estimation on stochastic processes
and smoothing by splines.
Ann. Math. Statist. ~ (1970), 495-502. (Zb 193, p. 452.)
37. Langhaar, H.L.; Chu, S.C.
Piecewise polynomials and the partition method for ordinary differential
equations.
Developments in theoretical and applied mechanics, Vol. 4 (Proc. Fourth
Southeastern Conf., New Orleans, La., 1968. Ed. by D. Frederick),
pp. 553-564. Pergamon Press, Oxford, 1970. (MR ~' 9447.)
38. Langner, w. Die Losung des Strakproblems bei empirischen Funktionen mittels stuck
weiser kubischer Polynome.
Elektron. Rechenanl. 12 (1970), 262-269. (BS )2, 3476.)
39. Lipow, P.R.
* Cardinal Hermite spline interpolation (doctoral dissertation).
University of Wisconsin, Madison, 1970. (DA 1!, 6128-B.)
40. Lucas, T.R.
* A theory of generalized splines with applications to nonlinear boundary
value problems (doctoral dissertation).
Georgia Institute of Technology, Atlanta, 1970. (DA 1!• 3555-B.)
41. Lucas, T.R.
A generalization of L-splines.
Numer. Math. iS (1970), 359-370. (MR 42, 3976; CA ~' 3295; BS 32, 1845.)
42. Marsaglia, G.
One-sided approximations by linear combinations of functions.
Approximation theory (Proc. Symp., Lancaster, July 1969. Ed. by
A. Talbot), pp. 233-242. Acad. Press, London, 1970.
(MR 42, 1307.)
43. Marsden, M.J.
An identity for spline functions with applications to variation
diminishing spline approximation.
J. Approximation Theory 1 (1970), 7-49. (MR 40, 7682; Zb 192, p. 421.)
- 46 -
44. Meinguet, J.
Optimal approximation and interpolation in normed spaces.
Numerical approximation to functions and data. Ed. by J.G. Hayes,
pp. 143-157. Athlone Press, London, 1970.
45. Natterer, F.
1970
Schranken fur die Eigenwerte gewohnlicher Differentialgleichungen durch
Spline-Approximation.
Numer. Math. ~ (1970), 346-354. (MR ~' 6413; Zb ~~ P• 184;
CA ~~ 2105.)
46. Nielson, G.M.
* Surface approximation and data smoothing using generalized spline func
tions (doctoral dissertation).
University of Utah, Salt Lake City, 1970. (DA ~~ 2833-B.)
47. Nilson, E.N.
Cubic splines on uniform meshes.
Comm. ACM ll (1970), 255-258. (BS ~~ 17930.)
48. Nitsche, J.
Lineare Spline-Funktionen und die Methoden von Ritz fur elliptische
Randwertprobleme.
Arch. Rational Mech. Anal. 36 (1970), 348-355. (MR 40, 8250;
Zb 192, p. 445.)
49. Nitsche, J.
Zur Konvergenz von Naherungsverfahren bezuglich verschiedener Normen.
Numer. Math. 15 (1970), 224-228. (BS 32, 1201.)
50. Parker, J.B.
Methods of graduating heterogeneous data.
Numerical approximation to functions and data. Ed. by J.G. Hayes,
pp. 111-114. Athlone Press, London, 1970. (CR ~~ 20514.)
51. Parker, K.
Experience with cubic splines in the graduation of neutron cross-section
data.
Numerical approximation to functions and data. Ed. by J.G. Hayes,
pp. 107-110. Athlone Press, London, 1970. (CR l!' 19959.)
- 47 - 1970
52. Popov, V.A.; Sendov, B.H.
Classes characterized by best-possible approximation by spline func
tions.
Mat. Zametki ~ (1970), 137-148 (Russian); translated as Math. Notes 8
(1970), 550-557. (Zb 201, p. 395.)
53. Powell, M.J.D.
Curve fitting by splines in one variable.
Numerical approximation to functions and data. Ed. by J.G. Hayes,
pp. 65-83. Athlone Press, London, 1970. (CR ll' 20157.)
54. Price, H.S.; Varga, R.S.
Error bounds for semidiscrete Galerkin approximations of parabolic
problems with applications to petroleum reservoir mechanics.
Numerical solution of field problems in continuum physics (SIAM-AMS
Proc.), vol. II, pp. 74-94. Amer. Math. Soc., Providence, R.I., 1970.
(MR 42, 1358.)
55. Rice, J.R.
General purpose curve fitting.
Approximation theory (Proc. Symp., Lancaster, July 1969. Ed. by
A. Talbot), pp. 191-204. Acad. Press, London, 1970.
(MR 42, 2632.)
56. Richards, F.B.
* A generalized minimum norm property for spline functions with applica
tions (doctoral dissertation).
University of Wisconsin, Madison, 1970. (DA ll' 6763-B.)
57. Ritter, K.
Two-dimensional spline functions and best approximations of linear
functionals.
J. Approximation Theory l (1970), 352-368. (Zb 203, p. 370.)
58. Rosman, B.H.
Extension of results by Rice and Schumaker on spline approximation.
SIAM J. Numer. Anal. 7 (1970), 314-316. (MR 42, 2633; Zb 208, p. 406;
CR ll' 20348.)
- 48 - 1970
59. Sakai, M.
Spline interpolation and two-point boundary value problems.
Mem. Fac. Sci. Kyushu Univ. Ser. A 24 (1970)~ 17-34. (Zb 201, p. 78;
BS 32, 1190.)
60. Sakai, M.
Multi-dimensional cardinal spline function and its applications.
Mem. Fac. Sci. Kyushu Univ. Ser. A 24 (1970), 40-46. (Zb 201, p. 78;
BS 32 , I 189. )
61. Sale, A.H.J.
Note on algorithm 42: Interpolation by certain quintic splines.
Comput. J. 13 (1970), 115.
62. Scherer, K.
On the best approximation of continuous functions by splines.
SIAM J. Numer. Anal. 2 (1970), 418-423. (MR 42, 2634; Zb 206, p. 348;
CA _!!:, 3287; BS 32, 1851 . )
63. Schoenberg, I.J.
A second look at approximate quadrature formulae and spline interpola
tion.
Advances in Math.~ (1970), 277-300. (MR ~' 8895; BS 32, 1211.)
64. Schoenberg, I.J.; Ziegler, z. On cardinal monosplines of least L
00-norm on the real axis.
J. Analyse Math. 23 (l970)s 409-436.
65. Schultz, M.H.
Elliptic spline functions and the Rayleigh-Ritz-Galerkin method.
Math. Comp. 24 (1970), 65-80. (MR ~' 9448; BS ~' 20282.)
66. Schultz, M.H.
Error bounds for polynomial spline interpolation.
Math. Comp. 24 (1970), 507-515. (CAll' 1420; BS 32, 5693.)
67. Schurer, F.
A note on interpolating periodic quintic spline functions.
Approximation theory (Proc. Symp., Lancaster, July 1969. Ed. by
A. Talbot), pp. 71-81. Acad. Press, London, 1970.
(MR 42, 757.)
- 49 -
67a. Sendov, B.; Popov, V.A.
Approximation with spline-functions (Russian).
C.R. Acad. Bulgare Sci. 23 (1970), 755-758. (Zb 209, p. 96.)
68. Shah, J.M.
Two-dimensional polynomial splines.
Numer. Math. 15 (1970), 1-14. (Zb ~, p. 176; CR l!• 20345;
CA .!.!' 2415.)
69. Subbotin, Yu.N.
Approximation of functions of class ~p by m-order splines. w
1970
Dokl. Akad. Nauk SSSR 195 (1970), 1039-1041 (Russian); translated
as Soviet Math. Dokl. ll (1970), 1626-1628. (BS ~' 3470.)
70. Subbotin, Yu.N.; Chernykh, N.I.
The order of the best spline approximations of certain classes of func
tions.
Mat. Zametki 7 (1970), 31-42 (Russian); translated as Math. Notes 7
(1970), 20-26. (MR ~' 4077; Zb 195, p. 351.)
71. Subbotin, Yu.N.
Diameter of class WrL in L(0,2n) and spline function approximation.
Mat. Zametki 7 (1970), 43-52 (Russian); translated as Math. Notes 7
(1970), 27-32. (MR ~' 4078; Zb 195, p. 71.)
72. Subbotin, Yu.N.
On a linear method for the approximation of differentiable functions.
Mat. Zametki 7 (1970), 423-430 (Russian); translated as Math. Notes 7
(1970), 256-260. (Zb 194, p. 367.)
73. Swartz, B.K.
* O(hk-j w (Dkf ,h)) bounds on some spline interpolation errors (doctoral
dissertation).
New York University, New York City, 1970. (DA 32, 441-B.)
74. Varga, R.S.
Accurate numerical methods for nonlinear boundary value problems.
Numerical solution of field problems in continuum physics (SIAM-AMS
Proc.), vol. II, pp. 152-167. Amer. Math. Soc., Providence, R.I., 1970.
(MR42, 2650.)
- 50 - 1970
75. Velikin, V.L.
Best approximations of continuous functions by spline functions.
Mat. Zametki ~ (1970), 41-46 (Russian); translated as Math. Notes 8
(1970), 492-495. (MR 42, 3474; Zb 205, p. 368.)
76. Woodford, C.H.
An algorithm for data smoothing using spline functions.
BIT .!..Q. (1970), 501-510. (CA_!i, 849.)
77. Young, J.D.
Function and first derivative fitting by modified quintic spline.
The Logistics Review ~' no. 27 ( 1970), 33-39.
78. Young, J.D.
An optimal cubic spline.
The Logistics Review ~, no. 29 (1970), 33-37.
79. Zafarullah, A.
A method of numerical solution of functional equations.
J. Optimization Theory Appl. 1 (1970), 283-288. (MR 42, 2702;
Zb ..!!!_, p • 1 9 1. )
- 51 -
Index of authors
The names of the authors of the enlisted publications are given here in
alphabetical order, together with a coded list of their papers. The meaning
of the compound numbers used as abbreviations of the papers is simply as
follows: the symbol 62-5, for instance, refers to a publication which ap
peared in 1962 and which has number 5 under that heading in the bibliography.
Ahlberg, J.H.
Akima, H.
Albasiny, E.L.
Amos, D.E.
Amunrud, L.R.
Anselone, P.M.
Asker, B.
Atkinson, K.E.
Atteia, M.
Aubin, J.P.
Barnhill, R.E.
Barrar, R.B.
Barrodale, I.
Bellman, R.
Bickley, W.G.
Birkhoff, G.
Birman, M.S. Blue, J.L.
Boor, C.R. de
Bramble, J.H.
Buchanan, J.E.
Bulirsch, R.
Carasso, c. Cavaretta, A.S. jr.
Chan, P.P.-Y.
Cheney, E.W.
(62-5; 63-1; 64-1; 65-1,2,3,4; 66-1; 67-1,2; 68-1;
69-1 ,2; 70-1 ,2) (70-2a)
(69-3)
(69-4)
(68-2)
(68-3)
(62-1)
(68-4)
(65-5,6; 66-2,3; 67-3,4; 68-5; 70-3)
(66-4; 67-5,6; 68-6,7)
(69-5)
(70-4)
(66-5)
(69-6)
(68-8; 69-7)
(60-1; 64-2; 65-7; 66-6; 67-7,8; 68-9,10; 69-8,9; 70-5)
(66-7)
(69-10)
(62-2; 63-2; 64-2; 65-7; 66-6,8,9; 68-11,12,13; 69-11)
(70-6, 7)
(68-14)
(68-15)
(66-10; 67-9,10,11,12,13,14; 69-12)
(70-8)
(70-9)
(68-16,53; 70-10,11)
Chernykh, N. I.
Cherruault, Y.
Chi, D.N.-H.
Chu, S.C.
(70-70)
(68-17)
(70-12)
(70-13,37)
- 52 -
Ciarlet, P.G. (66-11; 67-15; 68-18,19,20,21,22; 69-13; 70-14)
Collatz, L. (38-1; 64-3)
Covaci-Munteanu, M.J. (70-15)
Curry, H.B.
Curtis, A.R.
Cybertowicz, z.
Dailey, J.W.
Diringer, P.
Douglas, J. jr.
Dupont, T.
Eastman, W.L.
Ehlich, H.
Einarsson, B.
Elhay, s. Eltom, M.E.A. .. v Ermusa, A. E.
Esch, R.E.
Favard, J.
Ferguson, J.
Ferrand, C.
Fitzgerald, C. H.
Fix, G.
Freud, G.
Fyfe, D.J.
Gaier, D.
Galkin, P.V.
Garabedian, H.L.
Glass, J.M.
Gold, S.C.
(66-12)
(70-16)
(67-16; 68-23)
(69-14)
(68-24)
(70-17)
(70-17)
(69-16)
(66-13)
(68-25)
(69-15)
(68-26)
(68-32)
(69-16)
(40- J)
(64-4)
(67-17)
(69-17)
(68-27; 69-18,19;
(70-18)
(69-20; 70-19)
(70-20)
(70-21)
(60-1)
(66-14)
(70-22)
70-5)
Golomb, M.
Gordon, W.J.
Greville, T.N.E.
Griffith, B.A.
Hall, C.A.
Handscomb, D.C.
Hayes, J.G.
Heindl, G.
Herbold, R. J.
Hertling, J.
Hilbert, S.R.
Hill, I. D.
Holladay, J.C.
Hoskins, W.D.
Hulme, B.L.
Hung, H.-s.
Ikaunieks, E.A.
Innanen, K.A.
Ionescu, D.V.
Janenko, N.N.
Jerome, J.W.
Johnson, O.G.
Johnson, R.S.
Joly, J.L.
Kalik, C.
Karlin, S.
Karon, J.M.
Kautsky, J.
Kimeldorf, G.S. ""'" Korneicuk, N.P.
Krinzesza, F.
Kvasov, B. I.
- 53 -
(59-1; 68-28; 69-21)
(68-10; 69-22,23)
(64-5; 67-18; 69-24,25; 70-23)
(49-3)
(68-29; 69-26,27)
(66-15,16; 70-24)
(70-25)
(69-28)
(68-30; 69-29)
(70-26)
(69-30; 70-6)
(69-31)
(57-1)
(69-3; 70-27)
(68-31; 69-32)
(70-28)
(68-32)
(66-17)
(70-29)
(70-30)
(68-33; 69-33,34,35; 70-31)
(68-34; 69-36)
(60-2)
(67-19,20)
(70-32)
(66-18,19; 67-21,22; 68-35,36; 69-37,38; 70-33,34)
(68-36,37; 69-39; 70-33)
(70-35)
(70-36)
(69-39a)
(69-40)
(70-30)
Landis, F.
Langhaar, H.L.
Langner, W.
Lathrop, J.F.
Laurent, P.J.
Lee, J.W.
Lipow, P.R.
Loeb, H.L.
Loginov, A.S.
Loscalzo, F.R.
Love, A.E.H.
Lucas, T.R. v '(
Luspa~, N.E.
Lynch, R.E.
Malozemov, V.N.
Mangasarian, O.L.
Mansfield, L.E.
Marsaglia, G.
Marsden, M.J.
Mehlum, E.
Meinguet, J.
Meir, A.
Meyers, L.F.
Milnes, H. W.
Morin, M.
Munteanu, M.J.
Murty, V.N.
Natterer, F.
Nielson, G.M.
Nilson, E.N.
Nitsche, J.
Nord, S.
- 54 -
(62-3)
(70-37)
(70-38)
(69-41)
(68-3,38,39; 69-12,42)
(69-43; 70-34)
(70-39)
(70-4)
(69-44)
(67-23,24; 68-40; 69-45)
( 44-])
(70-40,41)
(69-39a)
(66-9)
(66-20; 67-25)
(69-46)
(69-47)
(70-42)
(66-2]; 68-41; 70-43)
(64-6)
(67-26; 70-44)
(66-28; 68-42,43; 69-48,83)
(50-1,2)
(66-22)
(69-49)
(67-27)
(69-50)
(69-51; 70-45)
(70-46)
(62-3,5; 63-1; 64-1; 65-1,2,3,4; 66-l; 67-1,2; 68-l;
69-l; 70-2,47)
(69-52,53,54,55,56; 70-48,49)
(67-28)
Parker, J.B.
Parker, K.
Perrin, F.M.
Petersen, I.
Phillips, G.M.
Pierce, J.G.
Popov, V.A.
Popoviciu, T.
Powell, M. J.D.
Price, H.S.
Price, K.H.
Priver, A.
Quade, W.
Reinsch, C.H.
Rice, J. R.
Richards, F.B.
Ritter, K.
Rivlin, T.J.
Rosman, B. H.
Roth, R.
Runge, C.
Rutishauser, H.
Sakai, M.
Sale, A.H.J.
Sard, A.
Schaback, R.
Schaefer, H.
Schatz, A.H.
Scherer, K.
Schoenberg, I.J.
- 55 -
(70-50)
(70-51)
(67-29; 69-57)
(62-4)
(68-44)
(69-58)
(70-18,52,67a)
(41-1)
(68-45; 69-59,60; 70-53)
(69-57; 70-54)
(70-1 1)
(67-8)
(38- 1)
(67-30)
(67-31; 69-61,62; 70-55)
(70-56)
(69-63,64; 70-57)
(69-65)
(70-58)
(69-6)
(04-J)
(60-3; 68-15)
(69-66; 70-59,60)
(70-6 1)
(49-1; 50-1,2; 63-3; 67-32; 68-46)
(69-67)
(63-4)
(70-7)
(70-62)
(46-1,2; 49-2; 53-1; 58-1; 64-7,8,9,10,11,12; 65-8;
66-12,21,23,24; 67-33; 68-47,48,49; 69-68,69,70,71;
70-63,64)
Schultz, M.H.
Schumaker, L.L.
Schurer, F.
Schweikert, D.G.
Schwerdtfeger, H.
Secrest, D.
Sendov, B.H.
Shah, J.M.
Sharma, A.
Shisha, 0.
Simpson, R.B.
Sims, S.E.
Slater, M.L.
Smirnov, V.M.
Sokolnikoff, I.S.
Solomj ak, M. Z.
Sonneveld, P.
Spath, H.
Starkweather, W.
Stephens, A.B.
Stern, M.D.
Storchai, V.F.
Strang, G.
Studden, W.J.
Subbotin, Yu.N.
Swartz, B.K.
Synge, J.L.
Talbot,. T.D.
Theilheimer, F.
Thomas, D.H.
Tihomirov, V.M.
- 56 -
(67-15,34; 68-9,19,20,21,22; 69-13,29,72,73,74,75,76,
77,78,79; 70-65,66)
(66-25; 67-21; 68-33,50,51; 69-17,34,35,46,80,81,82)
(68-16,52,53; 70-10,67)
(66-26,27)
(60-4; 61-1)
(65-9,10,11)
(70-52,67a)
(70-68)
(66-28; 68-42,43; et-41,Bl)
. (68-54)
(68-55)
(69-84)
(69-4)
(68-56)
(56-1)
(66-7)
(69-85)
(68-57; 69-86,87,88,89,90)
(61-2)
(69-91)
(66-29; 67-35)
(69-92)
(69-19)
(66-18; 68-58)
(67-36; 70-69,70,71,72)
(66-6; 68-59; 69-93; 70-73)
(49-3)
(67-23,24)
(61-2)
(68-14)
(69-94)
Van Arman, D.J.
Varga, R.S.
Velikin, V.L.
Wahba, G.
Wakoff, G. I.
Walsh, J.L.
Weinberger, H.F.
Wendroff, B.
Whitney, A.
Wixom, J.A.
Woodford, C.H.
Young, A.
Young, J.D.
Zafarullah, A.
Ziegler, z.
- 57 -
(68-58,60)
(66-30; 67-15,34; 68-9,19,20,21,22; 69-13,29,33,57,95;
70-14,54,74)
(70-75)
(70-36)
(69-96)
(62-5; 64-1; 65-1,2,4; 67-1,2; 68-1; 69-1)
(59-1; 61-3)
(65-12; 66-6; 69-93,97)
(49-2; 53-1)
(69-5)
(69-98; 70-76)
(66-5)
(67-37; 68-61,62; 69-99; 70-77,78)
(70-79)
(66-19; 67-22; 69-100; 70-64)