MINIMAL RESIDUAL RATIONAL KRYLOV SUBSPACE METHOD FOR SEQUENCES OF SHIFTED LINEAR SYSTEMS

The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there exist challenging scenarios for which there is still a lack of performant solvers. For instance, state-of-the-art procedures based on restarting may struggle to handle nonsymmetric problems where the shifts are possibly complex numbers that do not come as conjugate pairs. We design a novel projection strategy based on the rational Krylov subspace equipped with a minimal residual condition. We also devise a novel pole selection procedure, tailored to our problem, providing poles for the rational Krylov basis construction that yield faster convergence than those computed by available general-purpose schemes. A panel of diverse numerical experiments shows that our novel approach performs better than state-of-the-art techniques, especially on the very challenging problems mentioned above.