Enclosing all zeros of an analytic function - A rigorous approach

Tomas Johnson, Warwick Tucker

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23 Citations (Scopus)


We present a method to find all zeros of an analytic function in a rectangular domain. The approach is based on finding guaranteed enclosures rather than approximations of the zeros. Well-isolated simple zeros are determined fast and with high accuracy. Clusters of zeros can in many cases be distinguished from multiple zeros by applying the argument principle to sufficiently high-order derivatives of the function. We illustrate the proposed method through five examples of varying levels of complexity.

Original languageEnglish
Pages (from-to)418-423
Number of pages6
JournalJournal of Computational and Applied Mathematics
Issue number1
Publication statusPublished - 1 Jun 2009
Externally publishedYes


  • Argument principle
  • Interval analysis
  • Rigorous numerics
  • Root finding

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