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Re: Higher precision arithmetic ?

From: Chris Marks
Subject: Re: Higher precision arithmetic ?
Date: Wed, 7 Nov 2012 18:34:16 -0500

On Wed, Nov 7, 2012 at 5:10 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 ?

I doubt that higher resolution is the answer. I experienced a similar issue with corrosion current densities ranging over just a few orders of magnitude less. I implemented a weighting scheme so that 1  +/- 0.001 mA would be treated the same as 1 +/- 0.001 nA during the analysis. Increasing the resolution just lets the noise in the larger values dominate the model. If you provide more details, perhaps I can be more specific. I had other problems, including missing data, and never achieved completely satisfactory results.


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