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SingularValueDecomposition V6

• To: mathgroup at smc.vnet.net
• Subject: [mg100192] SingularValueDecomposition V6
• From: borisov at sas.upenn.edu
• Date: Thu, 28 May 2009 04:25:23 -0400 (EDT)

Hello,

In short: Is there a way to change the method in SingularValueDecomposition?
Explanation:
I have coded a relaxation scheme for solving a system of non-linear ODEs. The
relaxation scheme involves solving a linear system of algebraic equations in
the form S.b=-e. The matrix S is in my case 2000x2000. I use Krylov's method to
solve it. At certain conditions the system becomes unstable/singular. So I am
interested in finding the SVD for that Matrix. Unfortunately though the default
method is extermely slow. I couldn't find in the help which method for finding
the SVD is used, but by how slow it is I would assume it is the RQ method
(which goes like n^4). But I was told that method's like "divide and conquer"
go like n^3*Ln(n) and will be significantly faster (and I have been told there
are even faster methods). Is there a way to change the method in
SingularValueDecomposition?

In the end I could possibly use another method for resolving singularities
(S-mI).b=-e, but to evaluate m I still need to know what the maximum singular
value is. Will SingularValueList be sufficiently fast? Is there a way to change
the method there?

Best Regards
Alexander