FQMR: A flexible quasi-minimal residual method with inexact preconditioning

A flexible version of the QMR algorithm is presented which allows for the use of a different preconditioner at each step of the algorithm. In particular, inexact solutions of the preconditioned equations are allowed, as well as the use of an (inner) iterative method as a preconditioner. Several theo...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2002, Vol.23 (2), p.363-380
Main Authors: SZYLD, Daniel B, VOGEL, Judith A
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Exact sciences and technology
Experiments
Iterative methods
Mathematics
Methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
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Summary:A flexible version of the QMR algorithm is presented which allows for the use of a different preconditioner at each step of the algorithm. In particular, inexact solutions of the preconditioned equations are allowed, as well as the use of an (inner) iterative method as a preconditioner. Several theorems are presented relating the norm of the residual of the new method with the norm of the residual of other methods, including QMR and flexible GMRES (FGMRES). In addition, numerical experiments are presented which illustrate the convergence of flexible QMR (FQMR), and show that in certain cases FQMR can produce approximations with lower residual norms than QMR.
ISSN:1064-8275
1095-7197
DOI:10.1137/S106482750037336X