Quasi-analytical root-finding for non-polynomial functions

Cleonice F. Bracciali, Michael Carley

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A method is presented for the location of zeros of analytic
functions in the complex plane. The method is an extension of an
earlier technique for the real problem, and works by approximating
the function using a truncated Taylor series over regions of the
plane, and locating roots using a polynomial root-finding
method. These roots are then polished using Newton's method. The
plane is recursively subdivided to guarantee the accuracy of the
approximation to the function. The only requirement for the
root-finding method is that a means be available for evaluation of
the function and its derivatives. The method is demonstrated on a
simple test function and on realistic functions whose derivatives
are defined from a recursion relation and from a differential
Original languageEnglish
Pages (from-to)639-653
Number of pages15
JournalNumerical Algorithms
Issue number3
Early online date21 Feb 2017
Publication statusPublished - 30 Nov 2017


  • root-finding
  • analytic functions
  • complex roots


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