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Re: svd experts?

Thanks Dennis and Craig for the repsonses!

bob stockwell

Dennis Boccippio <djboccip@hotmail.com> wrote in message
> Not an SVD expert, but a while back I came across the following info
> when using SVD as an alternative to normal-equations solution of an
> overdetermined system:
> It is wise to scale A to have equal _column lengths_, particularly if
> the columns of A have very different numerical magnitudes (as might be
> obtained if A represented an instrument response kernel for inverting
> observations or fitting a model).  Thus, the SVD would be performed on
> Z, where:
> Z = A S^-1
> and S is a diagonal matrix consisting of the roots of the diagonal
> elements of A*A (A-transpose A).
> I can't recall what the motivation for this was; numerical stability or
> some issue unique to SVD use in overdetermined systems.
> I *believe* the reference for this is:
> Belsley, Kuh and Welch (1980): Regression Diagnostics, Identifying
> Influential Data and Sources of Collinearity, John Wiley & Sons, 292 pp.
> (SVD played of course a big part in their treatment of inversion of
> ill-conditioned matrices).
> If not, it may be:
> Draper and Smith (1981): Applied Regression Analysis.  John Wiley &
> Sons, 407 pp.
> Sorry for the ambiguity, it's been ~6 years since I had to deal with
> this and can't recall the exact reference...
> - Dennis Boccippio, NASA/MSFC SD-60