Colin McAuliffe <cjm2176 at columbia.edu> writes:
> Hello all,
>
> I am testing out a few linear solvers on a small (1052 by 1052)
> matrix. Using unpreconditioned GMRES with -ksp_gmres_restart 10000,
> GMRES still takes many times more than 1052 iterations to converge.
> Shouldn't it be the case that for a n by n matrix, n iterations of
> GMRES will give a full factorization of the matrix?
Yes, _in exact arithmetic_. This option will make orthogonalization
more stable:
-ksp_gmres_modifiedgramschmidt: Modified Gram-Schmidt (slow,more stable)
(KSPGMRESSetOrthogonalization)
the default is
-ksp_gmres_classicalgramschmidt: Classical (unmodified) Gram-Schmidt (fast)
(KSPGMRESSetOrthogonalization)
