Stepsize control for path tracking

Article

Abstract

Dedicated to our collaborator, mentor, and friend, Andrew Sommese, by Bates, Hauenstein, and Wampler on the occasion of his sixtieth birthday.

When numerically tracking implicitly-defined paths, such as is required for homotopy continuation methods, efficiency and reliability are enhanced by using adaptive stepsize and adaptive multiprecision methods. Both efficiency and reliability can be further improved by adapting precision and stepsize simultaneously. This paper presents a strategy for adjusting precision and stepsize together to eliminate certain types of path failures that can occur when adapting the two quantities independently, while also reducing the computational effort expended per unit advance along the path.

Attributes

Attribute NameValues
Creator
  • Charles Wampler II

  • Daniel Bates

  • Andrew Sommese

  • Jonathan Hauenstein

Journal or Work Title
  • Contemporary Mathematics

Volume
  • 496

First Page
  • 21

Publisher
  • American Mathematical Society

Date Created
  • 2016-11-03

Bibliographic Citation
Language
  • English

Departments and Units
Member of
Access Rights Open Access
Content License
  • All rights reserved

Digital Object Identifier

doi:10.7274/R08050JJ

This DOI is the best way to cite this article.

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