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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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**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *(continued)*
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Rik*, `2018/02/20`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Marco Caliari*, `2018/02/21`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Marco Caliari*, `2018/02/23`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *John W. Eaton*, `2018/02/23`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Rik*, `2018/02/26`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Marco Caliari*, `2018/02/27`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *John W. Eaton*, `2018/02/27`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Rik*, `2018/02/27`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Marco Caliari*, `2018/02/27`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Rik*, `2018/02/27`
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**,
*Marco Caliari* **<=**
**[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.**, *Rik*, `2018/02/28`