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Higher precision arithmetic ?

From: CdeMills
Subject: Higher precision arithmetic ?
Date: Wed, 7 Nov 2012 14:10:06 -0800 (PST)


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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