On the performance of various adaptive preconditioned GMRES strategies

This paper compares the performance on linear systems of equations of three similar adaptive accelerating strategies for restarted GMRES. The underlying idea is to adaptively use spectral information gathered from the Arnoldi process. The first strategy retains approximations to some eigenvectors from the previous restart and adds them to the Krylov subspace. The second strategy uses also approximated eigenvectors to define a preconditioner at each restart. This paper designs a third new strategy which combines elements of both previous approaches. Numerical results show that this new method is both more efficient and more robust.