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Unformatted text preview: U. Washington AMATH 352 - Winter 2010 Homework 3 - Due on 01/29/10 The first two exercises should be submitted via Scorelator (4 attempts are available). Remember to use the command save with the flag-ascii to output your results. Upload only your “.m” files. 1. (10 points) The goal of the exercise is to program the Jacobi method, which is a basic iterative algorithm to compute an approximate solution to a linear system Ax = b . The algorithm goes as follows • Set A , b , and ε . • Set the matrix D with the diagonal part of A . • Set x = . • Define r = b- Ax . • while k r k 2 > ε , – x = x + D- 1 r . – r = b- Ax . • end while The matrix D is a diagonal matrix with the same diagonal entries than A . The vector r is called the residual vector. Note that the residual is when x is equal to a solution. When the residual has a small norm, the corresponding vector x is an approximate solution. The Jacobi method computes such an approximate solution. Use the matrix and the right handJacobi method computes such an approximate solution....
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- Winter '07
- Linear Algebra, approximate solution, U. Washington