A GMRES(m) method with two stage deflated preconditioners

J. Shiroishi, T. Nodera

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The gmres(m) method is often used to compute Krylov subspace solutions of large sparse linear systems of equations. Morgan developed a new procedure that deflates the smallest eigenvalues and improves the eigenvalue distribution. Several preconditioning techniques have been explored in numerous research papers. In particular, the deflated GMRES proposed by Erhel and others replaces the smallest eigenvalues of the original coefficient matrix of the linear system with the largest modulus of the eigenvalues. We explore a new deflated gmres which uses a two stage deflation technique. Further, the results of the numerical experiments for test matrices are tabulated to illustrate that our approach is effective in solving a wide range of problems.

Original languageEnglish
JournalANZIAM Journal
Volume52
Publication statusPublished - 2010

Fingerprint

GMRES
Smallest Eigenvalue
Preconditioner
Deflation
Preconditioning Techniques
Eigenvalue Distribution
Sparse Linear Systems
Krylov Subspace
Linear system of equations
Modulus
Linear Systems
Numerical Experiment
Eigenvalue
Coefficient
Range of data

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

A GMRES(m) method with two stage deflated preconditioners. / Shiroishi, J.; Nodera, T.

In: ANZIAM Journal, Vol. 52, 2010.

Research output: Contribution to journalArticle

Shiroishi, J. ; Nodera, T. / A GMRES(m) method with two stage deflated preconditioners. In: ANZIAM Journal. 2010 ; Vol. 52.
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