An Efficient Family of Traub-Steffensen-Type Methods for Solving Systems of Nonlinear Equations. (2nd July 2014)

• Record Type: Journal Article
• Authors: Sharma, Janak Raj; Gupta, Puneet
• Other Names: Chen Zhangxin Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2014(2014)
• Publication Date: 2014-07-02
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2014/152187
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : Based on Traub-Steffensen method, we present a derivative free three-step family of sixth-order methods for solving systems of nonlinear equations. The local convergence order of the family is determined using first-order divided difference operator for functions of several variables and direct computation by Taylor's expansion. Computational efficiency is discussed, and a comparison between the efficiencies of the proposed techniques with the existing ones is made. Numerical tests are performed to compare the methods of the proposed family with the existing methods and to confirm the theoretical results. It is shown that the new family is especially efficient in solving large systems.