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Title: A technique for accelerating the convergence of restarted GMRES

Abstract

We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
15020368
Report Number(s):
UCRL-JRNL-202883
TRN: US200517%%526
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
SIAM Journal on Matrix Analysis and Applications
Additional Journal Information:
Journal Volume: 25; Journal Issue: 4
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; CONVERGENCE; IMPLEMENTATION; POLYNOMIALS; VECTORS

Citation Formats

Baker, A H, Jessup, E R, and Manteuffel, T. A technique for accelerating the convergence of restarted GMRES. United States: N. p., 2004. Web.
Baker, A H, Jessup, E R, & Manteuffel, T. A technique for accelerating the convergence of restarted GMRES. United States.
Baker, A H, Jessup, E R, and Manteuffel, T. 2004. "A technique for accelerating the convergence of restarted GMRES". United States. https://www.osti.gov/servlets/purl/15020368.
@article{osti_15020368,
title = {A technique for accelerating the convergence of restarted GMRES},
author = {Baker, A H and Jessup, E R and Manteuffel, T},
abstractNote = {We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.},
doi = {},
url = {https://www.osti.gov/biblio/15020368}, journal = {SIAM Journal on Matrix Analysis and Applications},
number = 4,
volume = 25,
place = {United States},
year = {Tue Mar 09 00:00:00 EST 2004},
month = {Tue Mar 09 00:00:00 EST 2004}
}