Abstract

We present a block MINRES algorithm for symmetric indefinite matrices
based on an alternate method for
constructing the block Lanczos vectors. This method allows us to compare
performance with the
standard MINRES algorithm iteration for iteration, and it handles
removal of dependent Lanczos vectors
more gracefully. We describe both a theoretical derivation of the
algorithm as well as practical implementation
details. Some numerical results are shown to illustrate performance
on some sample problems. We also
present some experiments to show how the relationship between right-hand
sides affects the performance
of this method.

Links

• http://arxiv.org/abs/1301.2102
• doi:10.1007/s11075-014-9907-z

BibTeX (Download)

@article{S.2013,
title = {A block MINRES algorithm based on the banded Lanczos method},
author = {Kirk M. Soodhalter},
url = {http://arxiv.org/abs/1301.2102},
doi = {10.1007/s11075-014-9907-z},
issn = {1017-1398},
year  = {2015},
date = {2015-01-01},
urldate = {2015-01-01},
journal = {Numerical Algorithms},
volume = {69},
issue = {3},
pages = {473-494},
abstract = {We present a block MINRES algorithm for symmetric indefinite matrices 
	based on an alternate method for 
	constructing the block Lanczos vectors. This method allows us to compare 
	performance with the 
	standard MINRES algorithm iteration for iteration, and it handles 
	removal of dependent Lanczos vectors 
	more gracefully. We describe both a theoretical derivation of the 
	algorithm as well as practical implementation 
	details. Some numerical results are shown to illustrate performance 
	on some sample problems. We also 
	present some experiments to show how the relationship between right-hand 
	sides affects the performance 
	of this method.},
keywords = {published},
pubstate = {published},
tppubtype = {article}
}