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https://issues.apache.org/jira/browse/MATH-602?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13084667#comment-13084667
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greg sterijevski commented on MATH-602:
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I agree. I been trying to cook up a nice illustration, but nothing that is
good enough yet.
In the meanwhile, the R manual has a good discussion which eloquently (at
least far more eloquently than me..) summarizes the usefulness of the
inverse condition number.
http://stat.ethz.ch/R-manual/R-devel/library/Matrix/html/rcond.html
Suffice it to say, having an index [0..1] is a bit more useful in comparing
matrices than an unbounded number.
-Greg
PS Will post a better example after I have concocted it.
> Inverse condition number
> ------------------------
>
> Key: MATH-602
> URL: https://issues.apache.org/jira/browse/MATH-602
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 2.2
> Environment: All
> Reporter: greg sterijevski
> Priority: Minor
> Labels: Condition, Inverse, Number
> Fix For: 3.0
>
> Attachments: svdinvcond, tstsvd
>
> Original Estimate: 1h
> Remaining Estimate: 1h
>
> In SingularValueDecompositionImpl, the condition number is given as the ratio
> of the largest singular value to the smallest singular value. While this is
> the correct calculation, because of concerns over rank deficiency,
> researchers have traditionally used the inverse of the condition number as a
> more stable indicator of rank deficiency.
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