×

Convergence analysis of Anderson-type acceleration of Richardson’s iteration. (English) Zbl 1463.65053

Summary: We consider Anderson extrapolation to accelerate the (stationary) Richardson iterative method for sparse linear systems. Using an Anderson mixing at periodic intervals, we assess how this benefits convergence to a prescribed accuracy. The method, named alternating Anderson-Richardson, has appealing properties for high-performance computing, such as the potential to reduce communication and storage in comparison to more conventional linear solvers. We establish sufficient conditions for convergence, and we evaluate the performance of this technique in combination with various preconditioners through numerical examples. Furthermore, we propose an augmented version of this technique.

MSC:

65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
PDFBibTeX XMLCite
Full Text: DOI