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Topic: Pseudoinverse in MATLAB
Replies: 12   Last Post: Mar 19, 2013 12:55 AM

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Bruno Luong

Posts: 8,845
Registered: 7/26/08
Re: Pseudoinverse in MATLAB
Posted: Mar 16, 2013 4:55 AM
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"Daniel Vasilaky" wrote in message <ki0nsg$q7e$1@newscl01ah.mathworks.com>...
> "Bjorn Gustavsson" <bjonr@irf.se> wrote in message
> %Instead of unstable, what I should have said is that the pinv() is a discontinuous function of the data.


It is missleading to say PINV is the problem, the cause is we are dealing with ill-posed system

A*x = y.

No one claims PINV is the best approach to solve ill-posed problem, it is actually a bad one. This is well known for decated (century?).

PINV has a strict mathematical definition.

The main usage if PINV is to provides x that minimizes the 2-norm |x|
subjected to |A*x - y| = min_z | A*z - y |.

It does NOT provide a stable solution x with respect to perturbation of y and A. It can be applied on many things, not exclusively for linear ill-posed system.

Bruno



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