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.
%0 Journal Article
%1 journals/siammax/BakerJM05
%A Baker, Allison H.
%A Jessup, Elizabeth R.
%A Manteuffel, Thomas A.
%D 2005
%J SIAM Journal on Matrix Analysis and Applications
%K 65f10-iterative-methods-for-linear-systems
%N 4
%P 962–984
%R 10.1137/S0895479803422014
%T A Technique for Accelerating the Convergence of Restarted GMRES
%U https://epubs.siam.org/doi/abs/10.1137/S0895479803422014
%V 26
%X 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.
@article{journals/siammax/BakerJM05,
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.},
added-at = {2019-04-16T05:36:37.000+0200},
author = {Baker, Allison H. and Jessup, Elizabeth R. and Manteuffel, Thomas A.},
biburl = {https://www.bibsonomy.org/bibtex/2f370bf419c3ee76ff7e19c26df2e8e44/gdmcbain},
doi = {10.1137/S0895479803422014},
ee = {http://dx.doi.org/10.1137/S0895479803422014},
interhash = {c2d7d0de1105aad8cc4f2ce1ad6b99d9},
intrahash = {f370bf419c3ee76ff7e19c26df2e8e44},
journal = {SIAM Journal on Matrix Analysis and Applications},
keywords = {65f10-iterative-methods-for-linear-systems},
number = 4,
pages = {962–984},
timestamp = {2019-04-16T05:36:37.000+0200},
title = {A Technique for Accelerating the Convergence of Restarted GMRES},
url = {https://epubs.siam.org/doi/abs/10.1137/S0895479803422014},
volume = 26,
year = 2005
}