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From: "Bjorn Gustavsson" <bjonr@irf.se>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Pseudoinverse in MATLAB
Date: Thu, 14 Mar 2013 09:21:17 +0000 (UTC)
Organization: Lancaster University
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"Daniel Vasilaky" wrote in message <khralp$bgq$1@newscl01ah.mathworks.com>...
> Elias Kyriakides <elias_kyriakides@hotmail.com> wrote in message <3AC15EAA.F5CACB12@hotmail.com>...
> > Dear friends,
> > 
> > Does anybody know how to get the actual code for the pseudoinverse in
> > MATLAB? I am really interested to see the whole thing plus the Singular
> > Value Decomposition SVD) and find out how it works.
> > 
> > I would be really grateful if somebody has it or knows how i can get it.
> > 
> > Thanks in advance,
> > Elias
> > 
> The SVD approach of pinv() is unstable.
> I developed an algorithm that solves the problem. It’s based on Tkhonov  regularization. 
>
If one goes down that route, I think the appropriate way is to first explicitly call SVD and then one can proceed from there with Tikhonov, damped SVD, truncated SVD or any other regularization, one can use generalised SVD if some pseudo-norm is preferable to stabilize the inverse. I don't see it as possible to present one single regularisation as the _right_ one for all cases, when one gets to such problems there is always some implicit (or explicit) knowledge as to what type of regularisation is appropriate that has to be taken into account.