Numerical Algorithms

, Volume 62, Issue 3, pp 429–444 | Cite as

A family of Steffensen type methods with seventh-order convergence

Original Paper

Abstract

In this paper, based on some known fourth-order Steffensen type methods, we present a family of three-step seventh-order Steffensen type iterative methods for solving nonlinear equations and nonlinear systems. For nonlinear systems, a development of the inverse first-order divided difference operator for multivariable function is applied to prove the order of convergence of the new methods. Numerical experiments with comparison to some existing methods are provided to support the underlying theory.

Keywords

Steffensen’s method Newton’s method Derivative free Seventh-order convergence Root-finding 

Mathematics Subject Classfications (2010)

65H05 65B99 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.College of SciencesNortheastern UniversityShenyangChina
  2. 2.Department of MathematicsBohai UniversityJinzhouChina

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