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Manuscript Title: Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives
Authors: C J Gillan, A Schuchinsky, I Spence
Program title: EZERO
Catalogue identifier: ADXY_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 175(2006)304
Programming language: Fortran 90.
Computer: IBM compatible desktop PC.
Operating system: Redhat Linux 9 Linux (with 2.4.18 kernel).
Word size: 32 bits
Keywords: Analytic functions, Zeros, Computation of zeros, Halley's method.
PACS: 02.30.Dk, 02.60.Cb, 02.70.Pt, 02.70.-c.
Classification: 4.7, 4.12.

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.

Solution method:
Our package uses the principle of the argument to count the number of zeros encompassed by a contour and then computes estimates for the zeros. Refined results for each zero are obtained by application of the derivative-free Halley method with or without Aitken aceleration, as the user wishes.

Running time:
Depends on number of roots for which one is solving. Typically 0.2 seconds per root on a Pentium IV.