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


  • A.N. Gromov


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.





Section 1. Numerical methods and applications

Author Biography

A.N. Gromov


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