Algorithm for finding eigenvalues

Mechanics, discrete, statistics, ...
Post Reply
thundre
Posts: 356
Joined: Sun Mar 27, 2011 9:01 am

Algorithm for finding eigenvalues

Post by thundre » Fri Jul 13, 2012 11:49 pm

Suppose I have a 20x20 matrix. All of the values are positive and rational. It's not symmetric.

I need the largest eigenvalue, or an approximation of it.

What algorithm should I be using?
Image

User avatar
jaap
Posts: 538
Joined: Tue Mar 25, 2008 3:57 pm
Contact:

Re: Algorithm for finding eigenvalues

Post by jaap » Sat Jul 14, 2012 5:03 am

I would try the Power Iteration method first. The reason is that it is conceptually very easy, and therefore almost trivial to implement and make work correctly. It is also one of the few algorithms that targets only the largest eigenvalue, and also works on non-symmetric matrices. Only if it were too slow would I start looking around for improvements or better algorithms.

thundre
Posts: 356
Joined: Sun Mar 27, 2011 9:01 am

Re: Algorithm for finding eigenvalues

Post by thundre » Mon Jul 16, 2012 6:39 pm

jaap wrote:I would try the Power Iteration method first.
Thanks, Jaap. That's exactly the kind of algorithm I was looking for. It has been 29 years since my last good math class in matrices.

Now I'm trying to find an elegant way of calculating the determinant. 20! terms is a lot. But there are a lot of repeated terms in the matrix, and any 4 in a square position will cancel, eliminating 2*18! terms from the total.

I'm also looking at LU decomposition.
Image

Post Reply