A class of exponential quadratically convergent iterative formulae for unconstrained optimization
type: Item
instance of: scholarly article
title: A class of exponential quadratically convergent iterative formulae for unconstrained optimization
zbMATH Open document ID: 1121.65067
author: Emin Kahya
published in: Applied Mathematics and Computation
publication date: 2007-06-06T00:00:00Z
review text: A nonlinear unconstraint optimization problem with an objective function depending: on one variable is considered. Three modifications of the Newton method for solving this problem are proposed. Each of the methods has an exponential iteration formula. It is proved that the proposed methods converge to the optimum solution with a quadratic order of convergence in a neighborhood of the optimum. The efficiency of the methods is analyzed using a criterion based on a comparison to the classical Newton method. Numerical experiments reported in the concluding part of the paper support obtained theoretical results and indicate that one of the exponential iterative formulae is from the point of view of its efficiency comparable to the classical Newton method.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 5161956
zbMATH Keywords: Newton method
zbMATH Keywords: exponential iterative formulae
zbMATH Keywords: quadratic convergence
zbMATH Keywords: nonlinear unconstraint optimization
zbMATH Keywords: numerical experiments
reviewed by: Karel Zimmermann
MaRDI profile type: Publication
full work available at URL: j.amc.2006.08.040
OpenAlex ID: W1963671310
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DOI: 10.1016/J.AMC.2006.08.040
description: scientific article; zbMATH DE number 5161956