[Trilinos-Users] [EXTERNAL] Anasazi solver with ML preconditioner won't converge

[Andris Freimanis]

Heidi,

yes, I used those two matrices only as a test. Actual matrices will be 
real SPD and much larger. An example of a small problem would be two 
37'500x37'500 size matrices, K with 7'916'526 elements and M with 37'500 
elements. I don't know if it helps, but I attached structure plots.

LOBPCG does seem like a better choice, as matrices will be large and 
I'll only need few (20-30 max) smallest eigenpairs. I rewrote my code 
and tried running it for 1 eigenpair with the same 48x48 matrices, 
LOBPCG also doesn't converge. I attached output and main.cpp file. Could 
this be because matrices are too small for this method?


2017.02.02. 19:57, Thornquist, Heidi K wrote:
> Hi Ray and Andris,
>
> I believe that the test matrix is the BCSSTK01/BCSSTM01 matrix pair from
> the BCSSTRUC1 set in Matrix Market.  That was just a guess from the
> statistics.  The convergence of this matrix pair can be affected by many
> things, including which eigenvalues you are looking for, the size of
> subspace, and the number of allowed iterations.  I think that the
> inclusion of the ML preconditioner may be obfuscating the issue.  It's
> easiest to reduce the complexity of the possibilities (i.e. remove the
> preconditioner) and see if you can something to converge for the simplest
> case, especially when the problem is so small.  Then start adding
> preconditioning, spectral transformations, etc. to speed up the solve and
> build more intuition about the solver.
>
> Since you are looking for the smallest eigenvalues and the system is SPD,
> have you also considered using LOBPCG?  Is this exercise with the Matrix
> Market test matrices in anticipation of a larger generalized eigenproblem
> with SPD matrices?  We can give guidance on how to solve this
> eigenproblem, but knowing what your final target will help us out.
>
> Thanks,
> Heidi
>

-- 
Andris Freimanis
PhD student

Riga Technical university
Institute of transporation
engineering

Ķīpsalas iela 6a, Rīga
00371 263 823 52
andris.freimanis_1 at edu.rtu.lv
www.rtu.lv

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