Method for the Calculation of all Zeros of an Analytic Function Based on
the Kantorovich Theorem

Vasyl Semenov

doi:10.1515/cmam-2014-0011

Published by De Gruyter April 24, 2014

Method for the Calculation of all Zeros of an Analytic Function Based on the Kantorovich Theorem

Vasyl Semenov

From the journal Computational Methods in Applied Mathematics

https://doi.org/10.1515/cmam-2014-0011

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Abstract.

We propose a method to calculate all zeros of an analytic function in a given rectangle. The main idea of our method is to construct a covering of the initial rectangle by subsets where either there are no zeros or the zero uniqueness test based on the Kantorovich theorem is satisfied. The algorithm for the construction of such covering is presented. The implementation of the method is shown on different examples.

Keywords: Non-linear Equation; Localization of Roots; Kantorovich Theorem; Taylor's Expansion

MSC: 65H10; 65H20

Received: 2014-1-11

Revised: 2014-4-1

Accepted: 2014-4-10

Published Online: 2014-4-24

Published in Print: 2014-7-1

Method for the Calculation of all Zeros of an Analytic Function Based on the Kantorovich Theorem

Abstract.

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