Re: svd experts?

[Dennis Boccippio <djboccip(at)hotmail.com>]

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




In article <V68_6.2448$nx3.1001188453@den-news1.rmi.net>,
 "R.G.S." <rgs1967@hotmail.com> wrote:

> Hail honourable svd experts,
> 
> I'm using svdc and svsol  to solve a matrix equation (like so).
> SVDC, A, W, U, V,/double
> result2 = SVSOL(U, W, V, data,/double)
> 
> Is it a good idea to scale my data so that the  A matrix
> is between a certain range? such as (0,1).
> I actually have julian day in there, so of course it seems
> wise to subract off a 'zero day' and bring the julian day into
> a normal range, but how important is it to scale the magnitude
> of the data?
> 
> I figure I'd try a quick "ask the audience" before trying to figure
> it out.
> 
> Thanks!
> 
> Cheers,
> bob stockwell
> 
>