[petsc-users] understand the restart number and total iteration number in GMRES

[Jed Brown]

GMRES provides a cheap estimate of the residual norm at each iteration.
In some cases ("happy breakdown") the iteration can't even proceed.  So
there is no point building a subspace of size m, then looking for a
solution.  Instead, just run until the estimated residual norm satisfies
the criteria, restarting with the current estimate of the solution as
initial guess any time the subspace would exceed dimension m.  This is
how everyone does restarted GMRES.

Mike Wick <michael.wick.1980 at gmail.com> writes:

> Hi:
>
> I am trying to understand the KSPGMRES a little more. In most books (or,
> Algorithm 4 in Saad's 1986 paper), I found that the GMRES(m) algorithm
> tries to construct a Krylov subspace with size m first, then seek for a
> solution that minimize over this space. Therefore, the total iteration
> number should be a multiple of the restart number.
>
> Apparently this is not the case in KSPGRMES. I wander if there is any
> stopping condition inside the restart algorithm, or if I misunderstand some
> part.
>
> Thanks!
>
> Mike