Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am writing various Gauss-Seidel algorithm parallel implementations using different programming techniques for my assignment.

I have created a MATLAB script for generating strictly diagonally dominant matrices with different degree of diagonal dominance and sparseness for testing my implementations.

Problem is that I can't find a way to generate matrix that requires more than 15 iterations to converge (epsilon is set to 0.0001).

Is there a property that makes a system GS-hard?

share|improve this question
1  
Probably you should consider asking this on SciComp. However, I would probably suggest looking at spectral properties including Condition Numbers. –  Inquest Mar 17 '12 at 20:04
    
If you mention the Hilbert matrix, people will think that you know what you are talking about. –  marty cohen Mar 18 '12 at 4:54

1 Answer 1

up vote 0 down vote accepted

A matrix with a high condition number will do the trick. One way to construct such a matrix is to create a diagonal matrix with a huge first entry and a tiny last entry and multiply it from both sides by random orthonormal matrices. The latter you can get by doing a QR decomposition of a random matrix.

share|improve this answer
    
In a pinch, QR decomposing a random matrix to generate a random orthogonal matrix works. There are more efficient methods (and equivalent), though... –  J. M. Mar 19 '12 at 17:04

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.