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

Odintsovo Branch of Moscow State Institute of International Relations of the Ministry of Foreign Affairs of the Russian Federation
• Senior Lecturer

References

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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

Vol. 18 (2017): Issue 2.

Section

Section 1. Numerical methods and applications

License

Copyright (c) 2017 Вычислительные методы и программирование

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This work is licensed under a Creative Commons Attribution 4.0 International License.