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[Octave-bug-tracker] [bug #53140] Solution of a system of linear equatio

From: Marco Caliari
Subject: [Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.
Date: Wed, 28 Feb 2018 02:41:24 -0500 (EST)
User-agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:58.0) Gecko/20100101 Firefox/58.0

Follow-up Comment #26, bug #53140 (project octave):

A single iterative refinement is

x = A \ b;
r = b - A * x;
xnew = x + (A \ r);

where of course A is factorized only once. The residual r has to be computed
in higher precision (I do not know the details). Iterative refinement is a
technique generally used in the solution of sparse linear system and it "may"
improve accuracy. If I set

Control (UMFPACK_IRSTEP) = 1;

instead of the default value 2, I can see a gain of about 10 seconds (20%).

I found a very similar thread here
https://github.com/JuliaLang/julia/issues/19500 with the same conclusions
(UMFPACK uses iterative refinements and wsolve does not really improve).

I would prefer to keep them, since other programs/languages use them. And add
an explicit description in the documentation, with the hint to rely on a
direct factorization is speed is more important than accuracy.


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