Increasing the interval of convergence for a generalized Newton’s method of solving nonlinear equations
DOI:
https://doi.org/10.26089/NumMet.v17r102Keywords:
iterative processes, Newton’s method, logarithmic derivative, continuous functions defined on a segment, higher order methods, interval of convergence, transcendental equationsAbstract
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.
References
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Published
25-01-2016
How to Cite
Громов А. 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
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Section
Section 1. Numerical methods and applications