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An Efficient Sixth-Order Newton-Type Method for Solving Nonlinear Systems

School of Mathematics and Physics, Bohai University, Jinzhou 121013, China
Department of Mathematics and Information Engineering, Puyang Vocational and Technical College, Puyang 457000, China
Author to whom correspondence should be addressed.
Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Algorithms 2017, 10(2), 45;
Received: 26 January 2017 / Revised: 8 April 2017 / Accepted: 20 April 2017 / Published: 25 April 2017
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems 2017)
PDF [407 KB, uploaded 25 April 2017]


In this paper, we present a new sixth-order iterative method for solving nonlinear systems and prove a local convergence result. The new method requires solving five linear systems per iteration. An important feature of the new method is that the LU (lower upper, also called LU factorization) decomposition of the Jacobian matrix is computed only once in each iteration. The computational efficiency index of the new method is compared to that of some known methods. Numerical results are given to show that the convergence behavior of the new method is similar to the existing methods. The new method can be applied to small- and medium-sized nonlinear systems. View Full-Text
Keywords: nonlinear systems; iterative method; Newton’s method; computational efficiency nonlinear systems; iterative method; Newton’s method; computational efficiency

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Wang, X.; Li, Y. An Efficient Sixth-Order Newton-Type Method for Solving Nonlinear Systems. Algorithms 2017, 10, 45.

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