Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems

Tony F. Chan*, Lisette De Pillis, Henk Van Der Vorst

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix-vector products per iteration without accessing AT. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal [15] (without look-ahead), which requires three matrix-vector products per iteration. We also present a related transpose-free version of the bi-conjugate gradients algorithm.

Original languageEnglish (US)
Pages (from-to)51-66
Number of pages16
JournalNumerical Algorithms
Volume17
Issue number1-2
DOIs
StatePublished - Jan 1 1998

Keywords

  • Bi-conjugate gradients algorithm
  • Krylov subspace methods
  • Lanczos algorithm
  • Nonsymmetric linear systems
  • Quasi-minimal residual algorithm

ASJC Scopus subject areas

  • Applied Mathematics

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