ISBN: 3-540-67162-5
TITLE: Computing the Zeros of Analytic Functions
AUTHOR: Kravanja, Peter; Barel, Marc Van
TOC:

1. Zeros of analytic functions 1
1.1 Introduction 1
1.1.1 Computing the total number of zeros with certainty 4
1.1.2 An overview of other approaches 8
1.2 Formal orthogonal polynomials 10
1.3 An accurate algorithm to compute zeros of FOPs 21
1.5 The software package ZEAL 34
1.5.1 The approach taken by ZEAL 35
1.5.2 The structure of ZEAL 37
1.5.3 ZEAL'S user interface 40
1.5.4 A few examples of how to use ZEAL 43
1.5.5 Concluding remarks 50
1.6 A derivative-free approach 51
2. Clusters of zeros of analytic functions 61
2.1 How to obtain the centre of a cluster and its weight 61
2.2 A numerical example 65
2.3 Rational interpolation at roots of unity 69
2.4 More numerical examples 79
3. Zeros and poles of meromorphic functions 83
3.1 Introduction 83
3.2 Theoretical considerations and numerical algorithm 85
3.3 A numerical example 88
4 Systems of analytic equations 91
4.1 Introduction 92
4.2 A multidimensional logarithmic residue formula 93
4.3 The algorithm 97
4.4 Numerical examples 10 1
References 10 5
END
