
Computing the Zeros of Analytic Functions
Springer (Publisher)
Published on 27. March 2000
Book
Paperback/Softback
VIII, 112 pages
978-3-540-67162-6 (ISBN)
Description
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.
More details
Series
Edition
2000 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 112 p.
Dimensions
Height: 233 mm
Width: 155 mm
Thickness: 7 mm
Weight
194 gr
ISBN-13
978-3-540-67162-6 (9783540671626)
DOI
10.1007/BFb0103927
Schweitzer Classification
Content
Zeros of analytic functions: Introduction.- Formal orthogonal polynomials.- An accurate algorithm to compute zeros of FOPs.- Numerical examples.- The software package ZEAL.- A derivative-free approach.-
Clusters of zeros of analytic functions: How to abtain the centre of a cluster and its weight.- A numerical example.- Rational interpolation at roots of unity.- More numerical examples.-
Zeros and ples of meromorphic functions: Introduction.- Theoretical considerations and numerical algorithm.- A numerical example.-
Systems of analytic equations: Introduction.- A multidimensional logarithmic residue formula.- The algorithm.- Numerical examples.