Computing the Zeros of Analytic Functions

Peter Kravanja, Marc Van Barel (auth.)9783540671626, 3540671625

Computing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable.

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Table of contents :
Zeros of analytic functions….Pages 1-59
Clusters of zeros of analytic functions….Pages 61-81
Zeros and poles of meromorphic functions….Pages 83-89
Systems of analytic equations….Pages 91-103