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[Octave-patch-tracker] [patch #9282] add minres for sparse linear system


From: Marco Caliari
Subject: [Octave-patch-tracker] [patch #9282] add minres for sparse linear systems
Date: Thu, 16 Mar 2017 05:13:04 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:52.0) Gecko/20100101 Firefox/52.0

Follow-up Comment #13, patch #9282 (project octave):

If you look at algorithm 9.1 on Saad's book, you see that the split
preconditioning for the conjugate gradient is realised at step 6. And it does
not matter whether the preconditioner M is M1*M2. The only thing to do is to
multiply the residual by inv(M). I see that Matlab always use a split
preconditioner:


A = toeplitz (1:4);
M = toeplitz ([2,1,0,0]);
b = A * ones (4, 1);
M2 = chol (M);
M1 = M2';
minres (A ,b ,0 ,1, M1, M2)
minres (A, b, 0, 1, M) % it should be exactly the same
M2 \ minres (M1 \ A / M2, M1 \ b, 0, 1) % equivalent formulation


I would remove the warning about too fast convergence. And some tests do not
work for me.


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