The document discusses two iterative methods for solving linear equation systems: Thomas method and Cholesky method. Thomas method is used for tridiagonal matrices and involves factorizing the matrix into lower and upper triangular matrices (L and U) and then solving for the vector D using L and then solving for the solution vector X using U. Cholesky method was also mentioned but not described.

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