Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian
Matrices. In: SIAM. J. Matrix Anal. and Appl., vol. 33-2, pp. 480-500, 2012.
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.
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BibTeX (Download)
@article{ESSSX.2012,
title = {Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian
Matrices},
author = {Mark Embree and Josef A. Sifuentes and Kirk M. Soodhalter and Daniel B. Szyld and Fei Xue},
url = {files/pdfs/Nearly-Herm.pdf},
doi = {10.1137/110825327},
year = {2012},
date = {2012-01-01},
urldate = {2012-01-01},
journal = {SIAM. J. Matrix Anal. and Appl.},
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.},
keywords = {published},
pubstate = {published},
tppubtype = {article}
}