[Numpy-discussion] Inversion of near singular matrices.
Algis Kabaila
akabaila at pcug.org.au
Sun Jan 30 21:05:56 EST 2011
>
> And if you are trying to solve a least-squares, I think that
> you should be using a ridge (or Tikhonov) regularisation:
> http://en.wikipedia.org/wiki/Tikhonov_regularization
> read in particular the paragraph above the table of content:
> you are most likely interested in Gamma = alpha identity,
> where you set alpha to be say 1% (or .1%) of the largest
> eigenvalue of A^t A.
>
> Gael
First of all I want to thank all who have contributed to this
discussion. It has been nothing less than inspiring! However,
it has drifted to areas in which I lack expertese and interest.
My interest is in structural analysis of engineering structures.
The structure response is generally characterised by a square
matrix with real elements. Actually, the structural engineer
has no interest in trying to invert a singular matrix. However
he/she is interested (or should be interested :) ) when the
square response matrix might approach singularity for this would
signal instability. He/She knows what the result of instability
would be - a disaster!
It is my fault not to have stated the problem with adequate
clarity and I intend to do that as soon as I can.
Thank you again for all your valuable contributions.
Al.
--
Algis
http://akabaila.pcug.org.au/StructuralAnalysis.pdf
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