An approach for constructing one-point iterative methods for solving nonlinear equations of one variable

Authors

  • A.N. Gromov Odintsovo University for the Humanities

DOI:

https://doi.org/10.26089/NumMet.v16r229

Keywords:

iterative processes, Newton’s method, logarithmic derivative, simple pole, contracted mapping, third order method, singular point, transcendental equations

Abstract

An approach for constructing one-point iterative methods for solving nonlinear equations of one variable is proposed. This approach is based on the concept of a pole as a singular point and on using Cauchy’s convergence criterion. It is shown that such an approach leads to new iterative processes of higher order with larger convergence domains compared to the known iterative methods. Convergence theorems are proved and convergence rate estimates are obtained. For polynomials having only real roots, the iterative process converges for any initial approximation to the sought root. Generally, in the case of real roots of transcendental equations, the convergence takes place when an initial approximation is chosen near the sought root.

Author Biography

A.N. Gromov

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

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Published

08-06-2015

How to Cite

Громов А. An Approach for Constructing One-Point Iterative Methods for Solving Nonlinear Equations of One Variable // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2015. 16. 298-306. doi 10.26089/NumMet.v16r229

Issue

Vol. 16 (2015): Issue 2.

Section

Section 1. Numerical methods and applications