The Systematic Formation of High-Order Iterative Methods
Department of Mathematics, Boston University, Boston, MA 02215, USA
- *Corresponding Author:
- Isaac Fried
Department of Mathematics, Boston University
Boston, MA 02215, USA
Tel: 1 617-353-2000
E-mail: [email protected]
Received Date: March 29, 2014; Accepted Date: May 09, 2014; Published Date: June 16, 2014
Citation: Fried I (2014) The Systematic Formation of High-Order Iterative Methods. J Appl Computat Math 3:165. doi: 10.4172/2168-9679.1000165
Copyright: © 2014 Fried I. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Fixed point iteration and the Taylor-Lagrange formula are used to derive, some new, efficient, high-order, up to octic, methods to iteratively locate the root, simple or multiple, of a nonlinear equation. These methods are then systematically modified to account for root multiplicities greater than one. Also derived, are super-quadratic methods that converge contrarily, and super-linear and super-cubic methods that converge alteratingly, enabling us, not only to approach the root, but also to actually bound and bracket it.