A block MINRES algorithm based on the banded Lanczos method (bibtex)
by Kirk Soodhalter
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.
Reference:
A block MINRES algorithm based on the banded Lanczos method (Kirk Soodhalter), In Numerical Algorithms, volume 69, 2015.
Bibtex Entry:
@ARTICLE{S.2013,
  author = {Soodhalter, Kirk},
  title = {A block MINRES algorithm based on the banded Lanczos method},
  journal = {Numerical Algorithms},
  year = {2015},
  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.},
  doi = {10.1007/s11075-014-9907-z},
  issn = {1017-1398},
  keywords = {paper},
  language = {English},
  owner = {kirk},
  timestamp = {2012.08.16},
  url = {http://arxiv.org/abs/1301.2102}
}
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