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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A preconditioned GMRES method for nonsymmetric or indefinite problems
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by Jinchao Xu and Xiao-Chuan Cai PDF
Math. Comp. 59 (1992), 311-319 Request permission


A preconditioning technique is proposed for nonsymmetric or indefinite linear systems of equations. The main idea in our theory, roughly speaking, is first to use some "coarser mesh" space to correct the nonpositive portion of the eigenvalues of the underlying operator and then switch to use a symmetric positive definite preconditioner. The generality of our theory allows us to apply any known preconditioners that were orginally designed for symmetric positive definite problems to nonsymmetric or indefinite problems, without losing the optimality that the original one has. Some numerical experiments based on GMRES are reported.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 311-319
  • MSC: Primary 65F30; Secondary 65F10, 65F35, 65N30
  • DOI:
  • MathSciNet review: 1134741