Heavy Ball Flexible GMRES Method for Nonsymmetric Linear Systems

Abstract

Flexible GMRES (FGMRES) is a variant of preconditioned GMRES, which changes preconditioners at every Arnoldi step. GMRES often has to be restarted in order to save storage and reduce orthogonalization cost in the Arnoldi process. Like restarted GMRES, FGMRES may also have to be restarted for the same reason. A major disadvantage of restarting is the loss of convergence speed. In this paper, we present a heavy ball flexible GMRES method, aiming to recoup some of the loss in convergence speed in the restarted flexible GMRES while keep the benefit of limiting memory usage and controlling orthogonalization cost. Numerical tests often demonstrate superior performance of the proposed heavy ball FGMRES to the restarted FGMRES.