Geodesic
A globally convergent method for finding zeros of integer functions of finite order
Numerical methods and programming, Tome 18 (2017) no. 2, pp. 115-128

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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.
Mots-clés : global convergence, partial fractions, Cauchy-Hadamard formula.
Keywords: logarithmic derivative, higher-order derivative 
@article{VMP_2017_18_2_a1,
     author = {A. N. Gromov},
     title = {A globally convergent method for finding zeros of integer functions of finite order},
     journal = {Numerical methods and programming},
     pages = {115--128},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_2_a1/}
}
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A. N. Gromov. A globally convergent method for finding zeros of integer functions of finite order. Numerical methods and programming, Tome 18 (2017) no. 2, pp. 115-128. http://geodesic.mathdoc.fr/item/VMP_2017_18_2_a1/