Thresholds of the inner steps in multi-step Newton method
type: Item
instance of: scholarly article
title: Thresholds of the inner steps in multi-step Newton method
zbMATH Open document ID: 1461.65089
published in: Algorithms
publication date: 2018-08-13T00:00:00Z
review text: Summary: We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after \(m\) steps) for solving nonlinear equations, \(F(x) = 0\), \(F:D \subseteq \mathbb R^n \rightarrow \mathbb R^n\). We highlight the following property of multi-step Newton method with respect to some other Newton-type method: for a given \(n\), there exist thresholds of \(m\), that is an interval \((m_i, m_s)\), such that for \(m\) inside of this interval, the efficiency index of multi-step Newton method is better than that of other Newton-type method. We also search for optimal values of \(m\).
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6916734
zbMATH Keywords: multi-step Newton method
zbMATH Keywords: efficiency index
zbMATH Keywords: threshold of inner steps
author: Şt. Măruşter
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a10030075
OpenAlex ID: W2725986460
cites work: Frozen jacobian iterative method for solving systems of nonlinear equations application to nonlinear IVPs and BVPs
cites work: Semilocal convergence by using recurrence relations for a fifth-order method in Banach spaces
cites work: Some Fourth Order Multipoint Iterative Methods for Solving Equations
cites work: Semilocal convergence of a sixth-order Jarratt method in Banach spaces
cites work: Q3343091
cites work: Q3925805
cites work: Q5652137
cites work: An optimization of Chebyshev's method
DOI: 10.3390/A10030075
description: scientific article; zbMATH DE number 6916734