Hybrid MPE-iterative schemes for linear and nonlinear systems (Q1382288)

The authors develop a minimal polynomial extrapolation method (MPE) for accelerating iterative methods and use it for solving a system of nonlinear equations, corresponding to finite difference discretization of a partial differential equation (a convection-diffusion problem). The Chebyshev method is taken as a test case for a linear method and a practical restart Chebyshev-MPE algorithm is proposed. The performance of the algorithm in the linear case and in the nonlinear case is tested.