)=O x tookouer2.l-2 - people.math.umass.edu
Transcript of )=O x tookouer2.l-2 - people.math.umass.edu
Maths 2118121
• HW #2 due 2,125 @ 9PM
•Read 3. I -3.3 for Tuesday
Find x such that fix)=Oin
non- linear
•tookouer2.l-2.SI
Condition and stability-
: Evaluate fan
¥¥¥¥*i:¥i¥Txmx*HIx⇒ K = OCI
) , well- conditioned
K >7 I ,Ill - conditioned
E± : fan= Txt- Tx , uniformly
well - conditioned
-
Kt Txt_rx=£¥c¥¥⇒
a) fan = Txt- Tx 4 -digit arithmetic
FCI 984 ) = ft - ifUNSTABLE
t.TT#xo2--0.4454xsubtractive -
cancellation= o .
ooo 1×102 = 0 . I 000 X to'
Fed's it
MATLFB-i.T-T4-0.1-39.i.XIO-I99.IR⑦ fan =#¥rxfa984)=oF¥¥ozFo.it#sxTFIyy5T.io--o.sgoeToi-"IIABLE
Evaluate fix,- +
\(
Y
well -conditioned Ill -conditionedI
Also:#\ABLE UNSTABLE
Ex : ax'tbxtC=o ⇒ x+,=-b±FX2A
a = O -
2MATLAB
Xt = 239.4247 . . . -6=-47.91 =3 -
c. = 6X-
= 0.1253 . . .. .
4-digitarithnet.ie subtractive
Xt,-re
To cancellation
2. (0.2)
a 41917¥23 f47.967,4285 ={¥÷¥
Ct)
~~ 0i)I-digit
Fix ? x-
tE÷÷÷4÷X-
=47.ci#FEEIoTI.e4IFsibO:l253nfall 4-digitaccuracy !
Floating Point Number Systems-
: fix)
X EIR , base B (typically 2), n
fl Cx) = I (O
.lo,be 63 .
- ton)p . Be*I OE bi E p -I ( B
- a 4913
Ht) to,to
(B -- co do, 1,2 , . .,93)
I i sign
A. bide - - ton)p : mantissa
e : exponent( - m seem)
Exe : f- 2 m
Imig = (O .I 00072×2-3=2-4--6.0625),o
Imax = (O
.II 111×23=(111.11--4.5),o
oulyaFINITE.name#of numbers are representable
Not pnnelgtresentddeRepresentabley#"""""""""""MBBBao Xmm Distribution Xmax It Density v
underflow overflow
IEEE754standard-flcxj.TT#EkTYantis Exponent
single precision(32 - bits) (
I,23,8)
double -
'
precision(64- bits) ( I >52,11
)
quadruple -precision(128-bits) ( 1,112,4)