Enclosing all zeros of an analytic function - A rigorous approach

Authors:
Tomas Johnson;Warwick Tucker
Affiliations:
Department of Mathematics, Uppsala University, Box 480, Uppsala, Sweden;Department of Mathematics, Uppsala University, Box 480, Uppsala, Sweden
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 4
Cited 1

Solving a Polynomial Equation: Some History and Recent Progress

SIAM Review
Evaluating derivatives: principles and techniques of algorithmic differentiation

Evaluating derivatives: principles and techniques of algorithmic differentiation
Automatic errorbounds for simple zeros of analytic functions

Communications of the ACM
Locating all the zeros of an analytic function in one complex variable

Journal of Computational and Applied Mathematics

Accelerating generators of iterative methods for finding multiple roots of nonlinear equations

Computers & Mathematics with Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

We present a method to find all zeros of an analytic function in a rectangular domain. The approach is based on finding guaranteed enclosures rather than approximations of the zeros. Well-isolated simple zeros are determined fast and with high accuracy. Clusters of zeros can in many cases be distinguished from multiple zeros by applying the argument principle to sufficiently high-order derivatives of the function. We illustrate the proposed method through five examples of varying levels of complexity.