Iterative methods
- 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