This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ACS I Linear Algebra Homework # 4 Due: Monday, 2/14 1. SOR Algorithm Write a code to implement the component form of the SOR method for a symmetric positive definite matrix. As a stopping criteria use bardbl vectorx k +1 − vectorx k bardbl 2 bardbl vectorx k +1 bardbl 2 ≤ 10 4 or a maximum number of steps of 500. Test your code for SOR on the linear system Avectorx = vector b . 4 6 8 2 6 10 16 6 8 16 36 20 2 6 20 15 1 2 3 4 = 48 98 228 134 using ω = 1, i.e., GaussSeidel. Use a starting point of vectorx = vector 0. a. Verify that A is positive definite. b. Use your SOR code to solve the given linear system for ω = 0 . 1 , . 2 , . . ., 1 . 9. Make a table outputting the following information: (i) ω , (ii) the number of iterations required to get to the given tolerance and (iii) ρ ( P ω ) where P ω is the iteration matrix for SOR for the given value of ω and ρ ( A ) denotes the spectral radius of the matrix A . (You can use Matlab to compute the spectral radius.) Plot ω . What is the optimal choice of ω for this problem? Relate this to ρ ( P ω ) and compare with theoretical results.) and compare with theoretical results....
View
Full
Document
This note was uploaded on 01/15/2012 for the course ISC 5315 taught by Professor Staff during the Spring '11 term at FSU.
 Spring '11
 staff

Click to edit the document details