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A Parallel Method of Verifying Solutions for Systems of Two Nonlinear Equations

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Parallel Processing and Applied Mathematics (PPAM 2019)

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

Abstract

The paper describes a new algorithm for verifying solutions of nonlinear systems of equations. Interval methods provide us a few tools for such verification. Some of them are based on topological theorems. Also our new test is based on checking the extendability of the function from a subspace of the boundary of the box to its interior. For a system of two equations, we can provide an efficient implementation. Generalization to a higher number of equations is also theoretically possible, yet cumbersome. Some numerical results are presented.

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Author information

Authors and Affiliations

  1. Department of Applied Informatics, Warsaw University of Life Sciences, ul. Nowoursynowska 159, 02-776, Warsaw, Poland

    Bartłomiej Jacek Kubica & Jarosław Kurek

Authors
  1. Bartłomiej Jacek Kubica
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  2. Jarosław Kurek
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Corresponding author

Correspondence to Bartłomiej Jacek Kubica .

Editor information

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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Kubica, B.J., Kurek, J. (2020). A Parallel Method of Verifying Solutions for Systems of Two Nonlinear Equations. 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_37

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  • DOI: https://doi.org/10.1007/978-3-030-43222-5_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43221-8

  • Online ISBN: 978-3-030-43222-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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