On a higher order secant method.
type: Item
instance of: scholarly article
title: On a higher order secant method.
zbMATH Open document ID: 1035.65057
DOI: 10.1016/S0096-3003(02)00257-6
published in: Applied Mathematics and Computation
publication date: 2003-09-15T00:00:00Z
review text: A modified secant method is introduced for solving a nonlinear equation \(f(x)=0\). The secant of \(f(x)\) at \(x_{k}\) is replaced by a higher order approximation. It is show that this method can have quadratic convergence as the Newton method. Global monotonic convergence is proven for real functions. In Banach space, the convergence is established with relaxed Kantorovich-Ostrowski type conditions. Numerical examples confirm the conclusions.
reviewed by: Zhen Mei
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1981456
zbMATH Keywords: secant method
zbMATH Keywords: Newton method
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: quadratic convergence
zbMATH Keywords: monotonic convergence
zbMATH Keywords: Banach space
zbMATH Keywords: numerical examples
author: Sergio Amat
author: S. Busquier
MaRDI profile type: Publication
cites work: A convergence theorem for Newton-like methods under generalized Chen- Yamamoto-type assumptions
cites work: Geometry and convergence of some third-order methods
cites work: A modification of the Kantorovich conditions for the secant method
cites work: Q5652137
cites work: The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
full work available at URL: s0096-3003(02)00257-6
OpenAlex ID: W2048658386
description: scientific article; zbMATH DE number 1981456