TY - JOUR
T1 - Some observations on weighted GMRES
AU - Güttel, Stefan
AU - Pestana, Jennifer
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: S.G. was supported by Deutsche Forschungsgemeinschaft Fellowship No. GU 1244/1-1. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2014/1/10
Y1 - 2014/1/10
N2 - We investigate the convergence of the weighted GMRES method for solving linear systems. Two different weighting variants are compared with unweighted GMRES for three model problems, giving a phenomenological explanation of cases where weighting improves convergence, and a case where weighting has no effect on the convergence. We also present a new alternative implementation of the weighted Arnoldi algorithm which under known circumstances will be favourable in terms of computational complexity. These implementations of weighted GMRES are compared for a large number of examples. We find that weighted GMRES may outperform unweighted GMRES for some problems, but more often this method is not competitive with other Krylov subspace methods like GMRES with deflated restarting or BICGSTAB, in particular when a preconditioner is used. © 2014 Springer Science+Business Media New York.
AB - We investigate the convergence of the weighted GMRES method for solving linear systems. Two different weighting variants are compared with unweighted GMRES for three model problems, giving a phenomenological explanation of cases where weighting improves convergence, and a case where weighting has no effect on the convergence. We also present a new alternative implementation of the weighted Arnoldi algorithm which under known circumstances will be favourable in terms of computational complexity. These implementations of weighted GMRES are compared for a large number of examples. We find that weighted GMRES may outperform unweighted GMRES for some problems, but more often this method is not competitive with other Krylov subspace methods like GMRES with deflated restarting or BICGSTAB, in particular when a preconditioner is used. © 2014 Springer Science+Business Media New York.
UR - http://hdl.handle.net/10754/599675
UR - http://link.springer.com/10.1007/s11075-013-9820-x
UR - http://www.scopus.com/inward/record.url?scp=84891719566&partnerID=8YFLogxK
U2 - 10.1007/s11075-013-9820-x
DO - 10.1007/s11075-013-9820-x
M3 - Article
SN - 1017-1398
VL - 67
SP - 733
EP - 752
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 4
ER -