Convergence analysis of Davidchack and Lai's algorithm for finding periodic orbits
type: Item
instance of: scholarly article
title: Convergence analysis of Davidchack and Lai's algorithm for finding periodic orbits
zbMATH Open document ID: 1024.37020
DOI: 10.1016/S0960-0779(00)00099-0
author: A. Klebanoff
author: Erik Bollt
published in: Chaos, Solitons and Fractals
publication date: 2003-03-19T00:00:00Z
review text: For an algorithm finding not necessarily stable periodic points of discrete dynamical systems in Euclidean space -- developed by Davidchack and Lai -- the authors give a rigorous proof of convergence and prove at least quadratic convergence. The algorithm is a modified Newton method which constitutes an almost implicit Euler method for a related differential equation, and contains sufficient parameters for adjustment to be applied to special cases in a flexible way, e.g. stabilizing the target points. A discussion of examples is included.
reviewed by: Dieter Erle
Mathematics Subject Classification ID: 37D05
Mathematics Subject Classification ID: 37C27
Mathematics Subject Classification ID: 65P40
zbMATH DE Number: 1884626
zbMATH Keywords: hyperbolic periodic orbits
zbMATH Keywords: numerical algorithm
zbMATH Keywords: basin of attraction
zbMATH Keywords: Newton method
zbMATH Keywords: switching matrix
describes a project that uses: Dynamics
MaRDI profile type: Publication
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full work available at URL: s0960-0779(00)00099-0
OpenAlex ID: W1996761923
description: scientific article; zbMATH DE number 1884626