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From "Remi Arntzen (JIRA)" <j...@apache.org>
Subject [jira] Updated: (MATH-157) Add support for SVD.
Date Thu, 02 Nov 2006 22:52:17 GMT
     [ http://issues.apache.org/jira/browse/MATH-157?page=all ]

Remi Arntzen updated MATH-157:
------------------------------

    Attachment: svd2.tar.gz

Now it works perfectly (At least according to how I think it should work).  However it is
not to your specifications, e.g. I do the eigenvector calculation on the larger of U and V
and then use the property M*v_i=q_i*u_i and M^T*u_i=q_i*v_i.  While I continue to learn more
about the properties of the SVD I will refine it as I go along, but right now I have to get
ready for school.

> Add support for SVD.
> --------------------
>
>                 Key: MATH-157
>                 URL: http://issues.apache.org/jira/browse/MATH-157
>             Project: Commons Math
>          Issue Type: New Feature
>            Reporter: Tyler Ward
>         Attachments: svd.tar.gz, svd2.tar.gz
>
>
> SVD is probably the most important feature in any linear algebra package, though also
one of the more difficult. 
> In general, SVD is needed because very often real systems end up being singular (which
can be handled by QR), or nearly singular (which can't). A good example is a nonlinear root
finder. Often the jacobian will be nearly singular, but it is VERY rare for it to be exactly
singular. Consequently, LU or QR produces really bad results, because they are dominated by
rounding error. What is needed is a way to throw out the insignificant parts of the solution,
and take what improvements we can get. That is what SVD provides. The colt SVD algorithm has
a serious infinite loop bug, caused primarily by Double.NaN in the inputs, but also by underflow
and overflow, which really can't be prevented. 
> If worried about patents and such, SVD can be derrived from first principals very easily
with the acceptance of two postulates.
> 1) That an SVD always exists.
> 2) That Jacobi reduction works. 
> Both are very basic results from linear algebra, available in nearly any text book. Once
that's accepted, then the rest of the algorithm falls into place in a very simple manner.


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