Efficient path tracking methods

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Abstract

Path tracking is the fundamental computational tool in homotopy continuation and is therefore key in most algorithms in the emerging field of numerical algebraic geometry. Though the basic notions of predictor-corrector methods have been known for years, there is still much to be considered, particularly in the specialized algebraic setting of solving polynomial systems. In this article, the effects of the choice of predictor method on the performance of a tracker is analyzed, and details for using Runge-Kutta methods in conjunction with adaptive precision are provided. These methods have been implemented in the Bertini software package, and several examples are described.

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Attribute NameValues
Creator
  • Daniel Bates

  • Andrew Sommese

  • Jonathan Hauenstein

Journal or Work Title
  • Numerical Algorithms

Volume
  • 58

Issue
  • 4

First Page
  • 451

Last Page
  • 459

Date Created
  • 2016-10-13

Bibliographic Citation
Language
  • English

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Record Visibility and Access Public
Content License
  • All rights reserved

Digital Object Identifier

doi:10.1007/s11075-011-9463-8

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