Enclosing all zeros of a system of analytic functions

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

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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
Publication statusPublished - 1 May 2019
Externally publishedYes


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

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