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Re: SingularValueDecomposition V6

• To: mathgroup at smc.vnet.net
• Subject: [mg100252] Re: SingularValueDecomposition V6
• From: Vladimir Marjanović <math.maniac.hr at gmail.com>
• Date: Fri, 29 May 2009 20:58:32 -0400 (EDT)
• References: <gvlhp1$djl$1@smc.vnet.net>

On Thu, 28 May 2009 08:25:05 +0000 (UTC), borisov at sas.upenn.edu wrote:

> 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

Here
http://reference.wolfram.com/mathematica/note/SomeNotesOnInternalImplementation.html#30506
you can find some explanations:
"SingularValueDecomposition uses the QR algorithm with Givens rotations.
PseudoInverse, NullSpace and MatrixRank are based on
SingularValueDecomposition. For sparse arrays, Arnoldi methods are used."



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