Comparison of some strategies for restarting GMRES

Abstract

Restarted Generalized Minimal Residual Method (GMRES(m)) is one of the most successful methods for solving linear system of equations [7]. At each cycle, GMRES(m) uses the residual at the previous cycle as starting guess, and constructs a Krylov subspace of dimension m with m n (where n is the dimension of the linear system) for computing a new residual, which is used as the starting residual for the next cycle, i.e., the next call to a GMRES routine. Rate of GMRES(m) convergence depends on an appropriate election of the restarting parameter m. In this context several algorithms have been proposed for choosing statically and dynamically the parameter m or introducing vectors for enriching the subspace.