Title: A derivative-free algorithm for computing zeros of analytic functions
Authors: Kravanja, Peter ×
Van Barel, Marc #
Issue Date: 1999
Publisher: Springer-verlag wien
Series Title: Computing vol:63 issue:1 pages:69-91
Abstract: Let W be a simply connected region in C, f : W --> C analytic in W and gamma a positively oriented Jordan curve in W that does not pass through any zero of f. We present an algorithm for computing all the zeros of f that lie in the interior of gamma. It proceeds by evaluating certain integrals along gamma numerically and is based on the theory of formal orthogonal polynomials. The algorithm requires only f and not its first derivative f'. We have found that it gives accurate approximations for the zeros. Moreover, it is self-starting in the sense that it does not require initial approximations. The algorithm works for simple zeros as well as multiple zeros, although it is unable to compute the multiplicity of a zero explicitly. Numerical examples illustrate the effectiveness of our approach.
ISSN: 0010-485X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science