Some new efficient multipoint iterative methods for solving nonlinear systems of equations

Abstract

It is attempted to put forward a new multipoint iterative method of sixth-order convergence for approximating solutions of nonlinear systems of equations. It requires the evaluation of two vector-function and two Jacobian matrices per iteration. Furthermore, we use it as a predictor to derive a general multipoint method. Convergence error analysis, estimating computational complexity, numerical implementation and comparisons are given to verify applicability and validity for the proposed methods.

Keywords:

• nonlinear systems
• multipoint iteration
• matrix
• LU factorization
• computational complexity

2010 AMS Subject Classifications:

• 65H10
• 65D30

Acknowledgements

We wish to sincerely thank the two anonymous referees for their recommendations, which have helped to the readability of this paper. The authors are also greatly indebted to Dr Fazlollah Soleymani for several helpful comments.

This research was supported by Islamic Azad University – Hamedan Branch, Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and Universitat Politècnica de València SP20120474.