On Fri, 7 Feb 2020 at 19:15, Fande Kong <[email protected]> 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
