Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points
Article (10.42Mb)Abstract
An optimal family of eighth-order multiple-zero finders and the dynamics behind their basins of attraction are proposed by considering modified Newton-type methods with multivariate weight functions. Extensive investigation of purely imaginary extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction. Numerical experiments strongly support the underlying theory pursued in this paper. An exploration of the relevant dynamics of the proposed methods is presented along with illustrative basins of attraction for various
polynomials.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
Related items
Showing items related by title, author, creator and subject.
-
A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points
(Elsevier Inc., 2016);A class of three-point sixth-order multiple-root finders and the dynamics behind their extraneous fixed points are investigated by extending modified Newton-like methods with the introduction of the multivariate weight ... -
On optimal fourth-order iterative methods free from second derivative and their dynamics
(2012);In this paper new fourth order optimal root-finding methods for solving nonlinear equations are proposed. The classical Jarratt’s family of fourth-order methods are obtained as special cases. We then present results which ... -
On developing a higher-order family of double-Newton methods with a bivariate weighting function
(Elsevier Inc., 2015);A high-order family of two-point methods costing two derivatives and two functions are developed by introducing a two-variable weighting function in the second step of the classical double-Newton method. Their theoretical ...
