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A Shaving Method for Interval Linear Systems of Equations

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Parallel Processing and Applied Mathematics (PPAM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8385))

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Abstract

We propose an iterative improvement method for an enclosure of the solution set of a system of interval linear equations. The method sequentially cuts off (shaves) parts of a given enclosure that contain no solution, yielding thus tighter enclosures. Since shaving can be done independently in the coordinates, the procedure is easily parallelized. Our approach is convenient for problems with wide input intervals, where traditional methods give poor enclosures. Finally, we present a limited computational study.

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Acknowledgments

M. Hladík was supported by CE-ITI (GAP202/12/G061) of the Czech Science Foundation. J. Horáček was supported by the Czech Science Foundation Grant P402-13-10660S, and by the Charles University grant GAUK N0. 712912.

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Authors and Affiliations

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

    Milan Hladík & Jaroslav Horáček

Authors
  1. Milan Hladík
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  2. Jaroslav Horáček
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Corresponding author

Correspondence to Milan Hladík .

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Editors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Department of Computer Science, Knoxville, Tennessee, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

  4. Technical University of Denmark Informatics and Mathematical Modelling, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Hladík, M., Horáček, J. (2014). A Shaving Method for Interval Linear Systems of Equations. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55195-6_54

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  • DOI: https://doi.org/10.1007/978-3-642-55195-6_54

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55194-9

  • Online ISBN: 978-3-642-55195-6

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