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https://issues.apache.org/jira/browse/MATH-355?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13049291#comment-13049291
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Christopher Nix commented on MATH-355:
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I've been having a think about this, though I'm far from an expert.
My understanding is as follows: The implementation in question applies the
Jacobi method to a matrix that has been pre-conditioned by QR-decomposition
(with perhaps an additional LQ-factorisation of the resulting R factor). This
gains a good start to the Jacobi method by localizing the Frobenius norm close
to the diagonal.
There are some clever steps in the analysis of the intermediate matrices as the
Jacobi method converges that I don't yet understand. However, as a starter, it
seems that an implementation of a Jacobi rotation and LQ-factorisation would be
useful.
I will gladly have a crack at these parts, since I can't spot anything
sufficient within the package at this time to do these things.
Any comments?
Chris
> State of the art SVD Algorithm
> ------------------------------
>
> Key: MATH-355
> URL: https://issues.apache.org/jira/browse/MATH-355
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 2.0, 2.1
> Reporter: Bruce A Johnson
> Labels: svd
> Fix For: 3.0
>
>
> There has been a lot of recent activity on the SVD algorithm for Commons
> Math. The SVD has also been in the news lately because of the development of
> a new algorithm that is both faster and more accurate than previous
> algorithms. Given the importance of the SVD in many applications it would be
> useful to have a Java implementation of this new algorithm in Commons Math.
> News article on the new algorithm:
> http://www.siam.org/pdf/news/1696.pdf
> Manuscripts on the new algorithm:
> http://www.netlib.org/lapack/lawnspdf/lawn169.pdf
> http://www.netlib.org/lapack/lawnspdf/lawn170.pdf
> Implementation in LAPACK 3.2.1
> dgesvj.f
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