Transformation methods for finding multiple roots of nonlinear equations
type: Item
instance of: scholarly article
title: Transformation methods for finding multiple roots of nonlinear equations
zbMATH Open document ID: 1205.65177
author: B. I. Yun
published in: Applied Mathematics and Computation
publication date: 2010-10-25T00:00:00Z
review text: The problem of finding a root of multiplicity \((m\geq 1)\) of a nonlinear equation on an interval \((a,b)\) is considered. The function \(f(x)\) is transformed to a hyper tangent function combined with a simple difference formula whose value changes from \((-1)\) to 1 as \((x)\) passes through the root of function. Then the so-called numerical integration method is applied to the transformed equation. A Steffensen-type iterative method which does not require any derivatives of \(f(x)\) nor is quite effected by an initial approximation is proposed. It is shown that the convergence order of the proposed method becomes cubic by simultaneous approximation to the root and its multiplicity.
reviewed by: Mykhaylo Pahirya
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 5804915
zbMATH Keywords: nonlinear equation
zbMATH Keywords: multiple root
zbMATH Keywords: multiplicity numerical integration method
zbMATH Keywords: Steffen\-sen-type iterative method
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.amc.2010.05.094
OpenAlex ID: W1989697284
cites work: New families of nonlinear third-order solvers for finding multiple roots
cites work: A third-order modification of Newton's method for multiple roots
cites work: A family of multiopoint iterative functions for finding multiple roots of equations
cites work: A secant method for multiple roots
cites work: A derivative-free transformation preserving the order of convergence of iteration methods in case of multiple zeros
cites work: New third order nonlinear solvers for multiple roots
cites work: High-order nonlinear solver for multiple roots
cites work: An optimal multiple root-finding method of order three
cites work: An improved method for finding multiple roots and it's multiplicity of nonlinear equations in \(\mathbb R\)
cites work: Q5732060
cites work: Quadratically convergent multiple roots finding method without derivatives
cites work: A non-iterative method for solving non-linear equations
cites work: A derivative free iterative method for finding multiple roots of nonlinear equations
DOI: 10.1016/J.AMC.2010.05.094
description: scientific article; zbMATH DE number 5804915