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https://issues.apache.org/jira/browse/MATH-157?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Brent Worden updated MATH-157:
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Fix Version/s: 1.2
> Add support for SVD.
> --------------------
>
> Key: MATH-157
> URL: https://issues.apache.org/jira/browse/MATH-157
> Project: Commons Math
> Issue Type: New Feature
> Reporter: Tyler Ward
> Assigned To: Luc Maisonobe
> Fix For: 1.2
>
> 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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