[Octave-bug-tracker] [bug #53140] Solution of a system of linear equations takes forever and hurts OS performance.

[Carlo de Falco]

Follow-up Comment #28, bug #53140 (project octave):

>> The residual r has to be computed in higher 
>> precision (I do not know the details).

@Marco, just for sake of complete information: the UMFPACK manual references
this paper for iterative refinement:

M. Arioli, J. W. Demmel, and I. S. Duff. 
Solving sparse linear systems with sparse backward error. 
SIAM J. Matrix Anal. Applic., 10:165–190, 1989.

which in turn cites

Skeel, R.D., 
Iterative Refinement Implies Stability for Gaussian Elimination.
Math. Comp, 35, 1980

and states that (under reasonable hypoteses)

"One step of iterative refinement is enough to guarantee that w [the
a-posteriori measure for the element-wise relative backward error] is small
[...] even if the the residual Ax-b is computed in the same arithmetic
precision as Gaussian elimination."

We might want to reference these papers in the docs.




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