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

  • Bartłomiej Jacek KubicaEmail author
  • Jarosław Kurek
Conference paper
  • 26 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Interval computations Nonlinear systems Verification Algebraic topology Extendability Multithreading 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Applied InformaticsWarsaw University of Life SciencesWarsawPoland

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