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On Single Precision Preconditioners for Krylov Subspace Iterative Methods

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Large-Scale Scientific Computing (LSSC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4818))

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Abstract

Large sparse linear systems Ax= b arise in many scientific applications. Krylov subspace iterative methods are often used for solving such linear systems. Preconditioning techniques are efficient to reduce the number of iterations of Krylov subspace methods. The coefficient matrix of the linear system is transformed into MA or AM in the left or right preconditioning, where M is a preconditioning matrix. In this paper, we analyze the influence of perturbation in the computation of preconditioning of Krylov subspace methods. We show that the perturbation of preconditioner does not affect the accuracy of the approximate solution when the right preconditioning is used. Some numerical experiments illustrate the influence of preconditioners with single precision arithmetic.

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Author information

Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Hiroto Tadano

  2. Department of Computer Science, University of Tsukuba, Tsukuba, 305-8573, Japan

    Tetsuya Sakurai

  3. Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Japan

    Hiroto Tadano & Tetsuya Sakurai

Authors
  1. Hiroto Tadano
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  2. Tetsuya Sakurai
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersen Plads, Building 321, DK-2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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© 2008 Springer-Verlag Berlin Heidelberg

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Tadano, H., Sakurai, T. (2008). On Single Precision Preconditioners for Krylov Subspace Iterative Methods. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_83

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  • DOI: https://doi.org/10.1007/978-3-540-78827-0_83

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78825-6

  • Online ISBN: 978-3-540-78827-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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