CS/MATH 3414 Assignment #8

Date Assigned: March 29, 2002
Date Due: April 3, 2002, in class, before class starts
  1. (10 points) For the 3-by-3 matrix 
    
[8 2 1
10 4 1
50 25 2]
    state (i) whether if it is diagonally dominant and (ii) whether the Gauss-Seidel method will converge.

  2. (10 points) Explain if the SOR method will converge (for 0 < w < 2) for the matrix given in Computer Problem 6.5.1 (a) (page 315) of your textbook. You do not have to do any programming; I am just using this question to identify the matrix. We almost finished solving this problem in class on Wednesday, March 27, 2002.

  3. (15+15=30 points) For the matrix given in Computer Problem 6.5.1 (d) (page 316) of your textbook, explain if the Jacobi and Gauss-Seidel methods will converge.

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