1. RUBEN DARIO ARISMENDI RUEDA

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

3. There are some kinds of Methods that are used to solve this lineal systems. 1- THOMAS 2-CHOLESKY

4. 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.

5. THIS METHOD WILL BE MORE CLEAR IF IS EXPLAINED WITH AN EXAMPLE. Basically this method uses the LU factorization. EXAMPLE. MATRIX ‘A’ R

6. THEN L*U=A MATRIX ‘L’ MATRIX ‘U’

7. L*D=R; By simple substitution the vector D is found. MATRIX ‘L’ * = D R

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

9. SOLUTION

10. 2-CHOLESKY. When is a simetric and definide matrix Then

12. EXAMPLE To understand this method, it will be easier with an example, that show how the Cholesky decomposition is made. MATRIX ‘A’ 6 15 55 15 55 225 55 225 979

14. 3. (k=3) and (i=1) (k=3) and (i=2)

15. Cholesky decomposition is L = 2,4495 6,1237 4,1833 22,454 20,916 6,1106