"A globally convergent method for finding zeros of integer functions of finite order"
Gromov A.N.

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.

Keywords: global convergence, logarithmic derivative, higher-order derivative, partial fractions, Cauchy-Hadamard formula.

  • Gromov A.N. – Moscow State Institute of International Relations at Odintsovo, Faculty of Economics; ulitsa Novo-Sportivnaya 3, Odintsovo, Moscow Region, 143007, Russia; Associate Professor, e-mail: an_gromov@rambler.ru