Two efficient derivative-free iterative methods for solving nonlinear systems
type: Item
instance of: scholarly article
title: Two efficient derivative-free iterative methods for solving nonlinear systems
zbMATH Open document ID: 1461.65092
author: Xiaofeng Wang
author: Xiaodong Fan
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 7042323
zbMATH Keywords: system of nonlinear equations
zbMATH Keywords: derivative-free iterative methods
zbMATH Keywords: order of convergence
zbMATH Keywords: high precision
describes a project that uses: MPFR
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a9010014
OpenAlex ID: W2253419173
cites work: Q5652137
cites work: Q5732060
cites work: A variant of Steffensen's method of fourth-order convergence and its applications
cites work: On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods
cites work: Frozen divided difference scheme for solving systems of nonlinear equations
cites work: Solving nonlinear integral equations of Fredholm type with high order iterative methods
cites work: Seventh-order derivative-free iterative method for solving nonlinear systems
cites work: A family of Steffensen type methods with seventh-order convergence
cites work: Q5627593
cites work: Analysing the efficiency of some modifications of the secant method
cites work: Ostrowski type methods for solving systems of nonlinear equations
cites work: A modified Newton-Jarratt's composition
cites work: Efficient high-order methods based on golden ratio for nonlinear systems
cites work: Q3343091
cites work: MPFR
cites work: Variants of Newton's method for functions of several variables
cites work: Increasing the order of convergence of iterative schemes for solving nonlinear systems
cites work: Solution of the Chandrasekhar H-equation by Newton’s Method
DOI: 10.3390/A9010014
description: scientific article; zbMATH DE number 7042323