数值分析session3.pptx

1Summary of last session -Chapter 4.Solving Systems of Linear Equationsn4.0.Introductionn4.1.Matrix Algebra:Basic Concepts,Elementary Operation,Equivalent System,Inverse Matrix.n4.2.LU Factorization:Easy to Solve System,LU Factorization,LDU Factorization,Doolittle Factorization,Crouts Factorization,Cholesky Factorization.24.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination34.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination44.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination54.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination64.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination74.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination84.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination94.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination104.3 Pivoting and Constructing Algorithm -Basic Gaussian Elimination114.3 Pivoting and Constructing Algorithm124.3 Pivoting and Constructing Algorithm134.3 Pivoting and Constructing Algorithm*-Theorem on Nonzero Pivots144.3 Pivoting and Constructing Algorithm*-Theorem on Nonzero Pivots154.3 Pivoting and Constructing Algorithm -LU-factorization164.3 Pivoting and Constructing Algorithm -LU-factorization174.3 Pivoting and Constructing Algorithm -LU-factorization184.3 Pivoting and Constructing Algorithm -Pivoting194.3 Pivoting and Constructing Algorithm -Pivoting204.3 Pivoting and Constructing Algorithm -Pivoting214.3 Pivoting and Constructing Algorithm -Pivoting 224.3 Pivoting and Constructing Algorithm -Pivoting234.3 Pivoting and Constructing Algorithm -Pivot Rows244.3 Pivoting and constructing Algorithm -Gaussian Elimination with Scaled Row Pivoting254.3 Pivoting and constructing Algorithm -Gaussian Elimination with Scaled Row Pivoting264.3 Pivoting and constructing Algorithm -Gaussian Elimination with Scaled Row Pivoting274.3 Pivoting and constructing Algorithm -Gaussian Elimination with Scaled Row Pivoting284.3 Pivoting and constructing Algorithm -Gaussian Elimination with Scaled Row Pivoting294.3 Pivoting and constructing Algorithm -Gaussian Elimination with Scaled Row Pivoting304.3 Pivoting and constructing Algorithm -Gaussian Elimination with Scaled Row Pivoting314.3 Pivoting and Constructing Algorithm -Factorizations PA=LUFactorizations PA=LU32Theorem 2:Theorem on LU Factorization of PA4.3 Pivoting and Constructing Algorithm -Factorizations PA=LUTheorem 3:Theorem on Solving PA=LU334.3 Pivoting and Constructing Algorithm -Diagonally Dominant Matrices344.3 Pivoting and Constructing Algorithm -Tridiagonal System 354.3 Pivoting and Constructing Algorithm -Tridiagonal System 364.3 Pivoting and Constructing Algorithm -Tridiagonal System 37Exercises