Two weighted eight-order classes of iterative root-finding methods

Abstract

In this paper we design, by using the weight function technique, two families of iterative schemes with order of convergence eight. These weight functions depend on one, two and three variables and they are used in the second and third step of the iterative expression. Dynamics on polynomial and non-polynomial functions is analysed and they are applied on the problem of preliminary orbit determination by using a modified Gauss method. Finally, some standard test functions are to check the reliability of the proposed schemes and allow us to compare them with other known methods.

Keywords:

• nonlinear equation
• iterative schemes
• optimal methods
• weight functions technique
• efficiency index

2010 AMS Subject Classifications:

• 65H05
• 65H10

Acknowledgements

This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and FONDOCYT 2011-1-B1-33 República Dominicana.