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Subsquares Approach – A Simple Scheme for Solving Overdetermined Interval Linear Systems

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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

In this work we present a new simple but efficient scheme – Subsquares approach – for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this scheme and discuss their features. We start with a simple algorithm as a motivation, then we continue with an improved algorithm. Both algorithms can be easily parallelized. The features of both algorithms will be discussed and numerically tested.

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Acknowledgement

Our research was supported by the grant GAČR P402/13/ 10660S. Jaroslav Horáček was partially supported by the Grant Agency of the Charles University (GAUK) grant no. 712912 and by GAUK no. SVV-2013–267313. Jaroslav Horáček would like to thank to Jezci mix-research group for general support.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Department of Applied Mathematics, Charles University, Prague, Czech Republic

    Jaroslav Horáček & Milan Hladík

Authors
  1. Jaroslav Horáček
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  2. Milan Hladík
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Corresponding author

Correspondence to Jaroslav Horáček .

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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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Horáček, J., Hladík, M. (2014). Subsquares Approach – A Simple Scheme for Solving Overdetermined Interval Linear Systems. 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_58

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  • DOI: https://doi.org/10.1007/978-3-642-55195-6_58

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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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