| Re: svd experts? [message #25540] |
Thu, 28 June 2001 07:32 |
R.G.S.
Messages: 46
Registered: September 2000
|
Member |
|
|
Thanks Dennis and Craig for the repsonses!
Cheers,
bob stockwell
Dennis Boccippio <djboccip@hotmail.com> wrote in message
news:djboccip-E005D8.01323127062001@news.mia.bellsouth.net.. .
> 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
>
>
|
|
|
|
| Re: svd experts? [message #25551 is a reply to message #25540] |
Tue, 26 June 2001 23:32  |
Dennis Boccippio
Messages: 23
Registered: July 2000
|
Junior Member |
|
|
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
>
>
|
|
|
|
| Re: svd experts? [message #25553 is a reply to message #25551] |
Tue, 26 June 2001 18:40 |
Craig Markwardt
Messages: 1869
Registered: November 1996
|
Senior Member |
|
|
"R.G.S." <rgs1967@hotmail.com> writes:
> Hail honourable svd experts,
I am not sure there are any SVD experts. :-(
You might have better luck on sci.math.num-analysis. There are some
really good people there. And your question is really a mathematics
question rather than an IDL question.
But my opinion is, yes, you should rescale if you can. In the best
world your matrix entries would be unitless.
Craig
--
------------------------------------------------------------ --------------
Craig B. Markwardt, Ph.D. EMAIL: craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
------------------------------------------------------------ --------------
|
|
|
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
