Hybrid MPE-iterative schemes for linear and nonlinear systems Original Research Article

The basic approach for the MPE (minimal polynomial extrapolation) method is introduced for use in conjunction with iterative methods. First, we develop a hybrid Chebyshev MPE algorithm and study its performance for a representative nonsymmetric linear system arising from a discretized two-dimensional convection-diffusion problem. A practical restart algorithm and supporting numerical studies are presented. Then, we consider the extension of the approach to nonlinear problems. In particular, we develop and test hybrid successive approximation MPE schemes for a class of nonlinear Poisson problems. The performance of these methods for a representative two-dimensional reaction-diffusion problem is investigated.