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