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Optimal Preconditioning for the Interval Parametric Gauss–Seidel Method

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Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9553))

Abstract

We deal with an interval parametric system of linear equations, and focus on the problem how to find an optimal preconditioning matrix for the interval parametric Gauss–Seidel method. The optimality criteria considered are to minimize the width of the resulting enclosure, to minimize its upper end-point or to maximize its lower end-point. We show that such optimal preconditioners can be computed by solving suitable linear programming problems. We also show by examples that, in some cases, such optimal preconditioners are able to significantly decrease an overestimation of the results of common methods.

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Acknowledgments

The author was supported by the Czech Science Foundation Grant P402-13-10660S.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Milan Hladík

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  1. Milan Hladík
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Correspondence to Milan Hladík .

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Editors and Affiliations

  1. Institute of Computer Science, University of Würzburg, Würzburg, Germany

    Marco Nehmeier

  2. Universität Würzburg, Würzburg, Germany

    Jürgen Wolff von Gudenberg

  3. Department of Mathematics, Uppsala University, Uppsala, Sweden

    Warwick Tucker

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Hladík, M. (2016). Optimal Preconditioning for the Interval Parametric Gauss–Seidel Method. In: Nehmeier, M., Wolff von Gudenberg, J., Tucker, W. (eds) Scientific Computing, Computer Arithmetic, and Validated Numerics. SCAN 2015. Lecture Notes in Computer Science(), vol 9553. Springer, Cham. https://doi.org/10.1007/978-3-319-31769-4_10

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  • DOI: https://doi.org/10.1007/978-3-319-31769-4_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31768-7

  • Online ISBN: 978-3-319-31769-4

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