ESCUELA DE INGENIERÍA DE PETROLEOS

RUBEN DARIO ARISMENDI RUEDA

ESCUELA DE INGENIERÍA DE PETROLEOS

CHAPTER 4: ‘Iterative Methods to solve lineal ecuation systems’

ESCUELA DE INGENIERÍA DE PETROLEOS

There are some kinds of Methods that are used to solve this lineal systems.

1- THOMAS

2-CHOLESKY

ESCUELA DE INGENIERÍA DE PETROLEOS

THOMAS.This method is used with a special kind of Matrix that has this form.

This is a special kind of matrix that has all it’s elements cero except that ones shown in the last picture.

ESCUELA DE INGENIERÍA DE PETROLEOS

THIS METHOD WILL BE MORE CLEAR IF IS EXPLAINED WITH AN EXAMPLE.Basically this method uses the LU factorization.

EXAMPLE.

MATRIX ‘A’ R

ESCUELA DE INGENIERÍA DE PETROLEOS

THEN L*U=A

MATRIX ‘L’

1,11,

−−− =

kk

kkk U

aL

kkkkkkk

kkk

ULbU

cU

,11,,

1,1

−−

−−

−==

MATRIX ‘U’

ESCUELA DE INGENIERÍA DE PETROLEOS

L*D=R; By simple substitution the vector D is found.

MATRIX ‘L’

* =

D R

ESCUELA DE INGENIERÍA DE PETROLEOS

U*X=D; By simple substitution the vector ‘X’ is found and the system will be solved.

MATRIX ‘U’

* =

X D

ESCUELA DE INGENIERÍA DE PETROLEOS

SOLUTION