Title
ZEAL : a mathematical software package for computing zeros of analytic functionsZEAL : a mathematical software package for computing zeros of analytic functions
Author
Faculty/Department
Faculty of Social Sciences. Communication Sciences
Research group
Faculty of Political and Social Sciences - other
Publication type
article
Publication
Amsterdam,
Subject
Computer. Automation
Source (journal)
Computer physics communications. - Amsterdam
Volume/pages
124(2000):2-3, p. 212-232
ISSN
0010-4655
ISI
000085195400008
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
We present a reliable and portable software package for computing zeros of analytic functions. The package is named ZEAL (ZEros of AnaLytic functions). Given a rectangular region W in the complex plane and a function f :W !C that is analytic in W and does not have zeros on the boundary of W, ZEAL localizes and computes all the zeros of f that lie inside W, together with their respective multiplicities. ZEAL is based on the theory of formal orthogonal polynomials. It proceeds by evaluating numerically certain integrals along the boundary of W involving the logarithmic derivative f 0 =f and by solving generalized eigenvalue problems. The multiplicities are computed by solving a linear system of equations that has Vandermonde structure. ZEAL is written in Fortran 90.
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