[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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