Solving Linear Equations on Parallel Distributed Memory Architectures by Extrapolation

Extrapolation methods can be used to accelerate the convergence of vector sequences. It is shown how three different extrapolation algorithms, the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE) and the modified minimal polynomial extrapolation (MMPE), can be used to solve systems of linear equations. The algorithms are derived and equivalence to different Krylov subspace methods are established. The extrapolation algorithms are to prefer on parallel distributed memory architectures since less inter-processor communication is needed