Re: Robust Inversion of a Matrix

On Thu, 28 Aug 2008 05:53:06 -0500, namlak wrote:

Hello,

i want to compute the inverse of a positive semi-definite matrix A. To
insure robustness of the inversion i want to use a simple
regularization
of the form:

A' = A + delta*I

where delta is the regularization parameter and A' is the regularized
matrix. Is anyone familiar with any empirical rules to determine delta
based on the values of the elements of the matrix A?

thank you,
N.

I think you're more likely to insure that the inverse of A' bears no
relation to the inverse of A.

The applied math newsgroup is really good, there are a lot more folks on

that group that really know their stuff compared to this one.

---
Tim Wescott
www.wescottdesign.com
Control and communications system consulting


I forgot to ask you: as far as i know you are an experienced dsp and
control systems engineer, where matrix inversion happens all the time. What
would you choose for delta? You know, there are various Tikhonov
regularization techniques but engineers do not seem to use them. Instead
they select delta on an ad-hoc basis. So, suppose that you run an
algorithm, which at each iteration inverts a positive semi-definite matrix.
Since the matrix can have a zero eigenvalue, and hence can be singular, you
do not have another choice but use regularization as i pointed. So, what
delta would you select?

N.
.

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