Computing the Zeros of Analytic Functions

• Main Authors: Kravanja, Peter (Author, http://id.loc.gov/vocabulary/relators/aut), Barel, Marc Van (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1727
• Subjects: Functions of complex variables.; Numerical analysis.; Functions of a Complex Variable.; Numerical Analysis.

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 blen...

Table of Contents:

• 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.