Iterative methods
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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.
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This document summarizes two iterative methods for solving linear equation systems: Thomas method and Cholesky decomposition. Thomas method uses LU factorization to solve tridiagonal matrices. Cholesky decomposition can solve symmetric and positive definite matrices by finding the lower triangular matrix L such that A = LLT. The document provides examples of applying each method to sample matrices to illustrate how they work.
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3) Mathematical models can be classified as linear or nonlinear, deterministic or probabilistic, static or dynamic, and lumped or distributed parameters.
Matrizinversa
El documento explica los pasos para calcular la matriz inversa. Primero, una matriz debe ser cuadrada y tener un determinante distinto de cero para tener una inversa. Luego, los pasos incluyen calcular la matriz de menores complementarios, obtener la matriz de adjuntos, transpónerla y multiplicarla por el inverso del determinante para encontrar la matriz inversa.
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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