Enclosing all zeros of a system of analytic functions

J. Dahne, M. F. Ciappina, W. Tucker

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We present a rigorous numerical method for location of simple zeros of a system of two analytic functions in a rectangular cuboid domain based on the logarithmic integral. We compare this to a simpler, also rigorous, method based on bisection. The latter is determined to be more efficient in the examples considered. This is mainly due to inefficient methods for computing the logarithmic integral occurring in the former method.

Original languageEnglish
Pages (from-to)513-522
Number of pages10
JournalApplied Mathematics and Computation
Volume348
DOIs
Publication statusPublished - 1 May 2019
Externally publishedYes

Keywords

  • Argument principle
  • Interval analysis
  • Rigorous numerics
  • Root finding
  • Systems of analytic functions

Cite this