[petsc-users] precondition for matrix-free GMRES

[Jed Brown]

On Tue, Apr 3, 2012 at 14:25, RenZhengYong <renzhengyong at gmail.com> wrote:

> I have a question to ask for your suggestions which is to solve Ax=b using
> GMRES,
> here A is partially dense.  Using petsc, I successfully used the
> matrix-free approach to solve
> it so that the expensive storage of A is avoided.  My question is could I
> offer an matrix B
> (which is sparse matrix and good approximation to A) so that the
> convergence rate of
> GMRES can be speed up.
>

Certainly, but the challenge is to find this other operator. You could try
sparse approximate methods to approximate either the operator or its
inverse. Other approaches would typically involve further knowledge of your
problem.
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