An approach for constructing one-point iterative methods for solving nonlinear equations of one variable
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.
Section
Section 1. Numerical methods and applications
Author Biography
A.N. Gromov
Odintsovo University for the Humanities, Department of Economics
• Associate Professor
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