[petsc-users] GMRES convergence

Jed Brown jedbrown at mcs.anl.gov
Thu Apr 18 11:46:24 CDT 2013

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)

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