Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Look-Ahead Procedures for Lanczos-Type Product Methods Based on Three-Term Lanczos Recurrences

by M. H. Gutknecht and K. J. Ressel

(Report number 1999-20)

Abstract
Lanczos-type product methods for the solution of large sparse non-Hermitian linear systems either square the Lanczos process or combine it with a local minimization of the residual. They inherit from the underlying Lanczos process the danger of breakdown. For various Lanczos-type product methods that are based on the Lanczos three-term recurrence, look-ahead versions are presented, which avoid such breakdowns or near breakdowns at the cost of a small computational overhead. Different look-ahead strategies are discussed and their efficiency is demonstrated by several numerical examples.

Keywords: Lanczos-type product methods, look-ahead, iterative methods,non-Hermitian matrices, sparse linear systems

@Techreport{GR99_254,
  author = {M. H. Gutknecht and K. J. Ressel},
  title = {Look-Ahead Procedures for Lanczos-Type Product Methods Based on Three-Term Lanczos Recurrences},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1999-20},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1999/1999-20.pdf },
  year = {1999}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).