The DEFLATED-GMRES(m, k) method with switching the restart frequency dynamically

Kentaro Moriya, Takashi Nodera

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


The DEFLATED-GMRES(m, k) method is one of the major iterative solvers for the large sparse linear systems of equations, Ax = b. This algorithm assembles a preconditioner adaptively for the GMRES(m) method based on eigencomponents gathered from the Arnoldi process during iterations. It is usually known that if a restarted GMRES(m) method is used to solve linear systems of equations, the information of the smallest eigencomponents is lost at each restart and the super-linear convergence may also be lost. In this paper, we propose an adaptive procedure that combines the DEFLATED-GMRES(m, k) algorithm and the determination of a restart frequency m automatically. It is shown that a new algorithm combining elements of both will reduce the negative effects of the restarted procedure. The numerical experiments are presented on three test problems by using the MIMD parallel machine AP3000. From these numerical results, we show that the proposed algorithm leads to faster convergence than the conventional DEFLATED-GMRES(m, k) method.

Original languageEnglish
Pages (from-to)569-584
Number of pages16
JournalNumerical Linear Algebra with Applications
Issue number7-8
Publication statusPublished - 2000 Jan 1


  • AP3000
  • Automatic restart
  • Deflated-GMRES
  • Preconditioning

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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