Basins of attraction for several methods to find simple roots of nonlinear equations
ThirdFourthMethods.pdf (1.854Mb)Abstract
There are many methods for solving a nonlinear algebraic equation. The methods are clas- sified by the order, informational efficiency and efficiency index. Here we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss several third and fourth order methods to find simple zeros. The relationship between the basins of attraction and the corresponding conjugacy maps will be discussed in numerical experiments. The effect of the extraneous roots on the basins is also discussed.
Description
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.
-
Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points
(Elsevier, 2018);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 ... -
Attractor basins of various root-finding methods
(Monterey, California. Naval Postgraduate School, 2001-06);Real world phenomena commonly exhibit nonlinear relationships, complex geometry, and intricate processes. Analytic or exact solution methods only address a minor class of such phenomena. Consequently, numerical approximation ... -
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 ...
