On developing a higher-order family of double-Newton methods with a bivariate weighting function
Abstract
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 and computational properties are fully
investigated along with a main theorem describing the order of convergence and the
asymptotic error constant as well as proper choices of special cases. A variety of concrete
numerical examples and relevant results are extensively treated to verify the underlying
theoretical development. In addition, this paper investigates the dynamics of rational iterative
maps associated with the proposed method and an existing method based on illustrated
description of basins of attraction for various polynomials.
Description
The article of record as published may be found at http://dx.doi.org/10.1016/j.amc.2014.12.130