DOI: https://doi.org/10.26089/NumMet.v18r209

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

Authors

  • A.N. Gromov

Keywords:

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

Abstract

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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Published

2017-03-23

Issue

Vol. 18 (2017): Issue 2.

Section

Section 1. Numerical methods and applications

Author Biography

A.N. Gromov

Odintsovo Branch of Moscow State Institute of International Relations of the Ministry of Foreign Affairs of the Russian Federation
• Senior Lecturer

References

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  3. W. He and N. Prabhu, “A Globally Convergent Method for Finding Zeros of Smooth Functions,” Appl. Math. Comput. 133 (2-3), 327-335 (2002).
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  6. G. I. Malashonok and A. A. Betin, “Computing of Complex Roots of Polynomials,” Vestn. Tambov Univ., Ser.: Estestv. Tekh. Nauki 13 (1), 138-141 (2008).
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