A Robust GMRES-Based Adaptive Polynomial Preconditioning Algorithm for Nonsymmetric Linear Systems

In this study a hybrid generalized minimal residual (GMRES)/polynomial preconditioning algorithm for solving nonsymmetric systems of linear equations is defined. The algorithm uses the results from cycles of restarted GMRES to form an effective polynomial preconditioner, typically resulting in decreased work requirements. The algorithm has the advantage over other hybrid algorithms in that its convergence behavior is well understood: the new algorithm converges for all starting vectors if and only if restarted GMRES converges. The results of numerical experiments with the algorithm are presented.