# Computing zeros of analytic functions in the complex plane without using derivatives

## Description

Abstract We present a package in Fortran 90 which solves f (z) = 0, where z ∈ W ⊂ C without requiring the evaluation of derivatives, f^′(z). W is bounded by a simple closed curve and f (z) must be holomorphic within W. We have developed and tested the package to support our work in the modeling of high frequency and optical wave guiding and resonant structures. The respective eigenvalue problems are particularly challenging because they require the high precision computation of all multiple complex ... Title of program: EZERO Catalogue Id: ADXY_v1_0 Nature of problem Finding solutions of the equation f(z)=0 where z is a variable in the complex plane and f(z) a function for which formulae for the first derivatives are either not easily obtainable or when such formulae are available are very expensive to compute repeatedly. For example suppose, f(z) is expressed as a determinant of a large matrix each element of which is an integral in which z is present in the integrand. Versions of this program held in the CPC repository in Mendeley Data ADXY_v1_0; EZERO; 10.1016/j.cpc.2006.04.007 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)