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Problem 2 programming excercise Consider the following mat.pdf

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This document describes a tridiagonal matrix A, defined by its elements aii=2, ai,i+1=1, and ai,i-1=1, that comes from the discretization of a differential equation. It specifies using Gauss-Seidel iteration with a tolerance of 10-5 to solve the system Ax=b, where b1=bn=1 and bi=0 for 1<i<n, for matrix sizes of n=10, n=20, and n=40. It asks to report the residuals and number of iterations for each n value and discuss how n affects the number of iterations.

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Problem 2 (programming excercise) Consider the following matrix (which comes from discretization of differential equation). A=(aij),aii=2(1in),ai,i+1=1(1in1), and ai,i1=1(2in). The matrix is tri-diagonal. In matlab, A=2diag(ones(n,1))+diag(ones(n1,1),1)+diag(ones(n1,1),1). For the right hand side, b1=bn=1,bi=01<i<n for solving Ax=b. Using Gauss-Seidel iterative method with tolerance 105 report the residuals and the number of iterations for n=10,n=20, and n=40. How does n affect the number of iterations?

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  • 1. Problem 2 (programming excercise) Consider the following matrix (which comes from discretization of differential equation). A=(aij),aii=2(1in),ai,i+1=1(1in1), and ai,i1=1(2in). The matrix is tri-diagonal. In matlab, A=2diag(ones(n,1))+diag(ones(n1,1),1)+diag(ones(n1,1),1). For the right hand side, b1=bn=1,bi=01<i<n for solving Ax=b. Using Gauss-Seidel iterative method with tolerance 105 report the residuals and the number of iterations for n=10,n=20, and n=40. How does n affect the number of iterations?