Increasing the interval of convergence for a generalized Newton’s method of solving nonlinear equations

Authors

  • A.N. Gromov Odintsovo University for the Humanities

DOI:

https://doi.org/10.26089/NumMet.v17r102

Keywords:

iterative processes, Newton’s method, logarithmic derivative, continuous functions defined on a segment, higher order methods, interval of convergence, transcendental equations

Abstract

An approach to the construction of an extended interval of convergence for a previously proposed generalization of Newton’s method to solve nonlinear equations of one variable. This approach is based on the boundedness of a continuous function defined on a segment. It is proved that, for the search for the real roots of a real-valued polynomial with complex roots, the proposed approach provides iterations with nonlocal convergence. This result is generalized to the case transcendental equations.

Author Biography

A.N. Gromov

Odintsovo University for the Humanities, Department of Economics
• Associate Professor

References

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  7. A. I. Markushevich, The Theory of Analytic Functions (Nauka, Moscow, 1967; Chelsea, New York, 1977).

Published

25-01-2016

How to Cite

Громов А.Н. Increasing the Interval of Convergence for a Generalized Newton’s Method of Solving Nonlinear Equations // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2016. 17. 7-12. doi 10.26089/NumMet.v17r102

Issue

Section

Section 1. Numerical methods and applications