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Improvements of Monotonicity Approach to Solve Interval Parametric Linear Systems

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Parallel Processing and Applied Mathematics (PPAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12044))

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Abstract

Recently, we have proposed several improvements of the standard monotonicity approach to solving parametric interval linear systems. The obtained results turned out to be very promising; i.e., we have achieved narrower bounds, while generally preserving the computational time. In this paper we propose another improvements, which aim to further decrease the widths of the interval bounds.

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Notes

  1. 1.

    All the methods used in the computation are based on revised affine forms.

  2. 2.

    We first substitute interval parameters by respective revised affine forms and then we performs computation of them.

  3. 3.

    For details on Interval-affine Gauss-Seidel iteration see [18].

  4. 4.

    Some attempts to use parallelization for increasing the efficiency of a few methods for solving interval parametric linear systems are described in [7].

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Acknowledgments

M. Hladík was supported by the Czech Science Foundation Grant P403-18-04735S.

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Authors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Iwona Skalna & Marcin Pietroń

  2. Charles University, Prague, Czech Republic

    Milan Hladík

Authors
  1. Iwona Skalna
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  2. Marcin Pietroń
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  3. Milan Hladík
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Corresponding author

Correspondence to Iwona Skalna .

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Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Southern California, Marina del Rey, CA, USA

    Ewa Deelman

  3. University of Tennessee, Knoxville, TN, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Skalna, I., Pietroń, M., Hladík, M. (2020). Improvements of Monotonicity Approach to Solve Interval Parametric Linear Systems. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12044. Springer, Cham. https://doi.org/10.1007/978-3-030-43222-5_33

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  • DOI: https://doi.org/10.1007/978-3-030-43222-5_33

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