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


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




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


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


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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



Section 1. Numerical methods and applications