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Re: Higher precision arithmetic ?

From: Ed Meyer
Subject: Re: Higher precision arithmetic ?
Date: Wed, 7 Nov 2012 20:46:21 -0800

On Wed, Nov 7, 2012 at 2:10 PM, CdeMills <address@hidden> wrote:

I'm busy with one "classical" engineering topic, i.e. modelling current in
micro-electronics devices. The main issue is that I have to deal with
variables which may span 8 orders of magnitude, like f.i. current going from
nano-amps to amps.

The computation succeeds, but at the end I have to invert a matrix whose
eigenvalues also span many orders of magnitude. I use a qr() decomposition,
followed by a call to chol2inv. Yet the result of chol2inv is sometimes not
full rank, while the result of qr() is.

Is there some way to get more resolution ? I.e. being able to compute the
inverse of matrices whose the ratio between the greatest and the smallest
eigenvalues module span 12 decades ?



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Perhaps we should add iterative refinement to the solver - it's cheap and it looks like it
would be easy.  I'd be willing to give it a try if you could supply me with your data to test
it.  I haven't played with lapack's refinement stuff on a really hard problem so I'm curious to
see how it does.  Oddly enough it doesn't look like matlab has iterative refinement

Ed Meyer

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