Convergence analysis of Anderson-type acceleration of Richardson's iteration

Lupo Pasini, Massimiliano

doi:10.1002/nla.2241

Convergence analysis of Anderson-type acceleration of Richardson's iteration

Journal Article · Wed Apr 03 00:00:00 EDT 2019 · Numerical Linear Algebra with Applications

DOI:https://doi.org/10.1002/nla.2241· OSTI ID:1511931

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Emory Univ., Atlanta, GA (United States). Dept. of Mathematics and Computer Science; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences

We consider here 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.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1511931

Journal Information:: Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Journal Issue: 4 Vol. 26; ISSN 1070-5325

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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