[petsc-users] Condition Number and GMRES iteration

[Lawrence Mitchell]

On Fri, 7 Feb 2020 at 19:15, Fande Kong <fdkong.jd at gmail.com> wrote:

> Thanks, Matt,
>
> It is a great paper. According to the paper, here is my understanding: for
> normal matrices, the eigenvalues of the matrix together with the
> initial residual completely determine the GMRES convergence rate. For
> non-normal matrices, eigenvalues are NOT the relevant quantities in
> determining the behavior of GMRES.
>
> What quantities we should look at for non-normal matrices? In other words,
> how do we know one matrix is easier than others to solve?
>

You need to do a field of values analysis to provide information. This can
give you bounds on convergence but it is often very weak.

Jörg Liesen has a bunch of papers on this.

Lawrence
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20200207/a8a56598/attachment.html>