A note on the convergence of the secant method for simple and multiple roots

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Title:	A note on the convergence of the secant method for simple and multiple roots
Author:	Díez, Pedro
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
Abstract:	The secant method is one of the most popular methods for root finding. Standard text books in numerical analysis state that the secant method is super linear: the rate of convergence is set by the gold number. Never- theless, this property holds only for simple roots. If the multiplicity of the root is larger than one, the convergence of the secant method becomes linear. This communication includes a detailed analysis of the secant method when it is used to approximate multiple roots. Thus, a proof of the linear convergence is shown. Moreover, the values of the corresponding asymptotic convergence factors are determined and are found to be also related with the golden ratio.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica -Numerical analysis -Secant method -Convergence rate -Asymptotic behavior -Anàlisi numèrica
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Document type:	Article - Submitted version Article
Published by:	Elsevier
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