Restarted GMRES preconditioned by deflation

Abstract

This paper presents a new preconditioning technique for solving linear systems. It is based on an invariant subspace approximation for the restarted GMRES algorithm. It uses the flexible GMRES scheme by designing a new preconditioning after each restart. Numerical examples show that this approach may converge almost as fast as full-GMRES at a, possibly, much lower cost.