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Workshop

Chebyshev Subdivision and Reduction Methods for Solving Multivariable Systems of Equations

  • Tyler Jarvis (Brigham Young University, Provo, USA)
Felix-Klein-Hörsaal Universität Leipzig (Leipzig)

Abstract

I present a new algorithm and Python implementation, YRoots, for finding isolated zeros of a system of real-valued smooth (not necessarily polynomial) functions in a bounded interval in R^n. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and elimination checks that leverage special properties of Chebyshev polynomials. The method has quadratic convergence locally near simple zeros of the system. It also finds all nonsimple zeros, but convergence to those zeros is not guaranteed to be quadratic.

Numerical evidence demonstrates that the method is both fast and accurate on a wide range of problems, significantly outperforming other standard methods on the problem of finding all real zeros in a bounded domain. YRoots is publicly available at github.com/tylerjarvis/RootFinding.

conference
29.07.24 02.08.24

MEGA 2024

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Christian Lehn

Ruhr-Universität Bochum

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Rainer Sinn

Universität Leipzig

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences

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