Paper Info
Title
A simpler GMRES and its adaptive variant for shifted linear systems.
Abstract
A variant of the simpler GMRES method is developed for solving shifted linear systems (SGMRES-Sh), exhibiting almost the same advantage of the simpler GMRES method over the regular GMRES method. Because the remedy adapted by GMRES-Sh is no longer feasible for SGMRES-Sh due to the differences between simpler GMRES and GMRES for constructing the residual vectors of linear systems, we take an alternative strategy to force the residual vectors of the add system also be orthogonal to the subspaces, to which the residual vectors of the seed system are orthogonal when the seed system is solved with the simpler GMRES method. In addition, a seed selection strategy is also employed for solving the rest non-converged linear systems. Furthermore, an adaptive version of SGMRES-Sh is presented for the purpose of improving the stability of SGMRES-Sh based on the technique of the adaptive choice of the Krylov subspace basis developed for the adaptive simpler GMRES. Numerical experiments demonstrate the benefits of the presented methods.
Year
DOI
Venue
2017
10.1002/nla.2076
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Keywords
Field
DocType
adaptive simpler GMRES,GMRES-Sh,seed selection strategy,SGMRES-Sh,shifted linear system,simpler GMRES
Krylov subspace,Residual,Mathematical optimization,Generalized minimal residual method,Linear system,Linear subspace,Mathematics
Journal
Volume
Issue
ISSN
24.0
1.0
1070-5325
Citations 
PageRank 
References 
4
0.40
12
Authors
3
Name
Order
Citations
PageRank
Yan-Fei Jing1679.48
Pei Yuan240.40
T. Z. Huang311518.95