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Practical Need for Algebraic (Equality-Type) Solutions of Interval Equations and for Extended-Zero Solutions

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Parallel Processing and Applied Mathematics (PPAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10778))

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Abstract

One of the main problems in interval computations is solving systems of equations under interval uncertainty. Usually, interval computation packages consider united, tolerance, and control solutions. In this paper, we explain the practical need for algebraic (equality-type) solutions, when we look for solutions for which both sides are equal. In situations when such a solution is not possible, we provide a justification for extended-zero solutions, in which we ignore intervals of the type \([-a,a]\).

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Acknowledgments

This work was supported in part by the grant DEC-2013/11/B/ST6/00960 from the National Science Center (Poland), by the US National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE-0926721, and by an award “UTEP and Prudential Actuarial Science Academy and Pipeline Initiative” from Prudential Foundation.

The authors are thankful to the anonymous referees for valuable suggestions.

Author information

Authors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Ludmila Dymova & Pavel Sevastjanov

  2. Computational Science Program, University of Texas at El Paso, El Paso, TX, 79968, USA

    Andrzej Pownuk & Vladik Kreinovich

Authors
  1. Ludmila Dymova
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  2. Pavel Sevastjanov
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  3. Andrzej Pownuk
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  4. Vladik Kreinovich
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Corresponding author

Correspondence to Andrzej Pownuk .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  3. University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Dymova, L., Sevastjanov, P., Pownuk, A., Kreinovich, V. (2018). Practical Need for Algebraic (Equality-Type) Solutions of Interval Equations and for Extended-Zero Solutions. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2017. Lecture Notes in Computer Science(), vol 10778. Springer, Cham. https://doi.org/10.1007/978-3-319-78054-2_39

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  • DOI: https://doi.org/10.1007/978-3-319-78054-2_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78053-5

  • Online ISBN: 978-3-319-78054-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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