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Polynomial iteration for nonsymmetric indefinite linear systems

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Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1230))

Abstract

We examine iterative methods for solving sparse nonsymmetric indefinite systems of linear equations. Methods considered include a new adaptive method based on polynomials that satisfy an optimality condition in the Chebyshev norm, the conjugate gradient-like method GMRES, and the conjugate gradient method applied to the normal equations. Numerical experiments on several non-self-adjoint indefinite elliptic boundary value problems suggest that none of these methods is dramatically superior to the others. Their performance in solving moderately difficult problems is satisfactory, but for harder problems their convergence is slow.

The work presented in this paper was supported by the U.S. Office of Naval Research under contract N00014-82-K-0814, by the U.S. Army Research Office under contract DAAG-83-0177 and by the Naval Underwater Systems Center Independent Research Project A70209.

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Authors and Affiliations

  1. Department of Computer Science, Yale University, New Haven, CT

    Howard C. Elman

  2. Naval Underwater Systems Center, New London, CT

    Roy L. Streit

Authors
  1. Howard C. Elman
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  2. Roy L. Streit
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Jean-Pierre Hennart

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© 1986 Springer-Verlag

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Elman, H.C., Streit, R.L. (1986). Polynomial iteration for nonsymmetric indefinite linear systems. In: Hennart, JP. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 1230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072674

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  • DOI: https://doi.org/10.1007/BFb0072674

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17200-0

  • Online ISBN: 978-3-540-47379-4

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