New efficient derivative free family of seventh-order methods for solving systems of nonlinear equations

New efficient derivative free family of seventh-order methods for solving systems of nonlinear... We present a three-step two-parameter family of derivative free methods with seventh-order of convergence for solving systems of nonlinear equations numerically. The proposed methods require evaluation of two central divided differences and inversion of only one matrix per iteration. As a result, the proposed family is more efficient as compared with the existing methods of same order. Numerical examples show that the proposed methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Algorithms Springer Journals

New efficient derivative free family of seventh-order methods for solving systems of nonlinear equations

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Computer Science; Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis
ISSN
1017-1398
eISSN
1572-9265
D.O.I.
10.1007/s11075-016-0254-0
Publisher site
See Article on Publisher Site

Abstract

We present a three-step two-parameter family of derivative free methods with seventh-order of convergence for solving systems of nonlinear equations numerically. The proposed methods require evaluation of two central divided differences and inversion of only one matrix per iteration. As a result, the proposed family is more efficient as compared with the existing methods of same order. Numerical examples show that the proposed methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations.

Journal

Numerical AlgorithmsSpringer Journals

Published: Jan 12, 2017

References

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