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Re: Higher precision arithmetic ?

From: c.
Subject: Re: Higher precision arithmetic ?
Date: Wed, 7 Nov 2012 23:44:48 +0100

On 7 Nov 2012, at 23:10, CdeMills wrote:

> Hello,
> I'm busy with one "classical" engineering topic, i.e. modelling current in
> micro-electronics devices.

cool! what problem are you dealing with in particular? 
are you aware of the packages in Octave-Forge for simulating 
electonic devices (secs1d, secs2d, secs3d) and circuits (ocs)?
do you you think you might be able to contribute some of your code there?

> 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.

that's not much in principle, the electron density in a diode can easily 
have a range of values spanning about 20 orders of magnitude and can be treated
reasonably well with double precision floating point numbers.

> 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 ?

except some really really special extreme cases, the best way to deal with such
problems is to redesign your algorithm so that it is less sensitive on 
errors. So are you really sure yours is such a VERY special case? Can you 
more details about it?

> Regards
> Pascal

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