Conjugate gradient and minimal residual methods for solving symmetric indefinite systems

Yu Ling Lai*, Wen-Wei Lin, Dan'l Pierce

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Norm-minimizing-type methods for solving large sparse linear systems with symmetric and indefinite coefficient matrices are considered. The Krylov subspace can be generated by either the Lanczos approach, such as the methods MINRES, GMRES and QMR, or by a conjugate-gradient approach. Here, we propose an algorithm based on the latter approach. Some relations among the search directions and the residuals, and how the search directions are related to the Krylov subspace are investigated. Numerical experiments are reported to verify the convergence properties.

Original languageEnglish
Pages (from-to)243-256
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume84
Issue number2
DOIs
StatePublished - 28 Oct 1997

Keywords

  • Conjugate gradient
  • Krylov subspace
  • Minimal residual
  • Symmetric indefinite systems

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