Computing the zeros of analytic functions
The authors study the zeros of analytic function and several related problems in computational complex analysis. Using a logarithmic residue based quadrature method, the authors develop the algorithm for computing all the zeros of an analytic function \(f\) that lie inside a positively oriented Jordan curve \(\gamma.\) The same method is used to approximate the center of a cluster and the total number of zeros of the analytic function in this cluster. The authors also show how the logarithmic residue based approach can be used to compute all the zeros and poles of a meromorphic function that lie in the interior of a Jordan curve. They consider systems of analytic equations and use a multidimensional logarithmic residue formula to compute the zeros and corresponding multiplicities of analytics functions. This book provides useful methods and software for computing zeros of analytic functions which leads to a rich blend of mathematics and numerical analysis.
scientific article; zbMATH DE number 1446983