Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems

In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divi...

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Main Authors:	Xiaofeng Wang, Xiaodong Fan
Format:	Article
Language:	English
Published:	MDPI AG 2016-02-01
Series:	Algorithms
Subjects:	system of nonlinear equations derivative-free iterative methods order of convergence high precision
Online Access:	http://www.mdpi.com/1999-4893/9/1/14

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spelling	doaj-203f18da1ba5478d99b36d92656857422020-11-24T20:49:03ZengMDPI AGAlgorithms1999-48932016-02-01911410.3390/a9010014a9010014Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear SystemsXiaofeng Wang0Xiaodong Fan1School of Mathematics and Physics, Bohai University, Jinzhou 121013, ChinaSchool of Mathematics and Physics, Bohai University, Jinzhou 121013, ChinaIn this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Numerical experiments support the theoretical results. Experimental results show that the new methods remarkably reduce the computing time in the process of high-precision computing.http://www.mdpi.com/1999-4893/9/1/14system of nonlinear equationsderivative-free iterative methodsorder of convergencehigh precision
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xiaofeng Wang Xiaodong Fan
spellingShingle	Xiaofeng Wang Xiaodong Fan Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems Algorithms system of nonlinear equations derivative-free iterative methods order of convergence high precision
author_facet	Xiaofeng Wang Xiaodong Fan
author_sort	Xiaofeng Wang
title	Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems
title_short	Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems
title_full	Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems
title_fullStr	Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems
title_full_unstemmed	Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems
title_sort	two efficient derivative-free iterative methods for solving nonlinear systems
publisher	MDPI AG
series	Algorithms
issn	1999-4893
publishDate	2016-02-01
description	In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Numerical experiments support the theoretical results. Experimental results show that the new methods remarkably reduce the computing time in the process of high-precision computing.
topic	system of nonlinear equations derivative-free iterative methods order of convergence high precision
url	http://www.mdpi.com/1999-4893/9/1/14
work_keys_str_mv	AT xiaofengwang twoefficientderivativefreeiterativemethodsforsolvingnonlinearsystems AT xiaodongfan twoefficientderivativefreeiterativemethodsforsolvingnonlinearsystems
_version_	1716806968592564224

Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems

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