A globally convergent method for finding zeros of integer functions of finite order

Authors

  • A.N. Gromov Odintsovo Branch of Moscow State Institute of International Relations of the Ministry of Foreign Affairs of the Russian Federation

DOI:

https://doi.org/10.26089/NumMet.v18r209

Keywords:

global convergence, logarithmic derivative, higher-order derivative, partial fractions, Cauchy–Hadamard formula

Abstract

A method for finding zeros of integer functions of finite order is proposed. This method converges to a root starting from an arbitrary initial point and, hence, is globally convergent. The method is based on a representation of higher-order derivatives of the logarithmic derivative as a sum of partial fractions and reduces the finding of a root to the choice of the minimum number from a finite set. The rate of convergence is estimated.

Author Biography

A.N. Gromov

References

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  7. A. I. Markushevich, The Theory of Analytic Functions (Nauka, Moscow, 1967; Chelsea, New York, 1977).

Published

23-03-2017

How to Cite

Громов А.Н. A Globally Convergent Method for Finding Zeros of Integer Functions of Finite Order // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2017. 18. 115-128. doi 10.26089/NumMet.v18r209

Issue

Section

Section 1. Numerical methods and applications