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

Abstract

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.

Authors:
ORCiD logo [1]
  1. 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
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1511931
Alternate Identifier(s):
OSTI ID: 1504993
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Numerical Linear Algebra with Applications
Additional Journal Information:
Journal Name: Numerical Linear Algebra with Applications; Journal ID: ISSN 1070-5325
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Anderson acceleration; fixed-point scheme; projection method; Richardson iteration

Citation Formats

Lupo Pasini, Massimiliano. Convergence analysis of Anderson-type acceleration of Richardson's iteration. United States: N. p., 2019. Web. doi:10.1002/nla.2241.
Lupo Pasini, Massimiliano. Convergence analysis of Anderson-type acceleration of Richardson's iteration. United States. doi:10.1002/nla.2241.
Lupo Pasini, Massimiliano. Wed . "Convergence analysis of Anderson-type acceleration of Richardson's iteration". United States. doi:10.1002/nla.2241.
@article{osti_1511931,
title = {Convergence analysis of Anderson-type acceleration of Richardson's iteration},
author = {Lupo Pasini, Massimiliano},
abstractNote = {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.},
doi = {10.1002/nla.2241},
journal = {Numerical Linear Algebra with Applications},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {4}
}

Journal Article:
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This content will become publicly available on April 3, 2020
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