by Mark Embree, Josef A. Sifuentes, Kirk M. Soodhalter, Daniel B. Szyld, Fei Xue
Abstract:
The progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residual-minimizing short-recurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a low-rank skew-Hermitian part. We analyze this algorithm, observing a critical instability that makes the method unsuitable for some problems. To work around this issue we introduce a different short-term recurrence method based on Krylov subspaces for such matrices, which can be used as either a solver or a preconditioner. Numerical experiments compare this method to alternative algorithms.
Reference:
Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices (Mark Embree, Josef A. Sifuentes, Kirk M. Soodhalter, Daniel B. Szyld, Fei Xue), In SIAM. J. Matrix Anal. and Appl., volume 33-2, 2012.
Bibtex Entry:
@ARTICLE{ESSSX.2012,
author = {Embree, Mark and Sifuentes, Josef A. and Soodhalter, Kirk M. and
Szyld, Daniel B. and Xue, Fei},
title = {Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian
Matrices},
journal = {SIAM. J. Matrix Anal. and Appl.},
year = {2012},
volume = {33-2},
pages = {480-500},
abstract = {The progressive GMRES algorithm, introduced by Beckermann and Reichel
in 2008, is a residual-minimizing short-recurrence Krylov subspace
method for solving a linear system in which the coefficient matrix
has a low-rank skew-Hermitian part. We analyze this algorithm, observing
a critical instability that makes the method unsuitable for some
problems. To work around this issue we introduce a different short-term
recurrence method based on Krylov subspaces for such matrices, which
can be used as either a solver or a preconditioner. Numerical experiments
compare this method to alternative algorithms.},
doi = {10.1137/110825327},
keywords = {paper},
owner = {kirk},
timestamp = {2012.08.16},
url = {files/pdfs/Nearly-Herm.pdf}
}