How to Improve the Domain of Starting Points for Steffensen's Method

We analyze the semilocal convergence of Steffensen's method, using a novel technique, which is based on recurrence relations, for solving systems of nonlinear equations. This technique allows analyzing the convergence of Steffensen's method to solutions of equations, where the function inv...

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Bibliographic Details
Published in:	Studies in applied mathematics (Cambridge) Vol. 132; no. 4; pp. 354 - 380
Main Authors:	Ezquerro, J. A., Hernández-Verón, M. A.
Format:	Journal Article
Language:	English
Published:	Cambridge Blackwell Publishing Ltd 01-05-2014
Subjects:	Applied mathematics Convergence Expansion Functions (mathematics) Mathematical analysis Nonlinear equations Studies
Online Access:	Get full text
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Summary:	We analyze the semilocal convergence of Steffensen's method, using a novel technique, which is based on recurrence relations, for solving systems of nonlinear equations. This technique allows analyzing the convergence of Steffensen's method to solutions of equations, where the function involved can be both differentiable and nondifferentiable. Moreover, this technique also allows enlarging the domain of starting points for Steffensen's method from certain predictions with the simplified Steffensen method.
Bibliography:	ark:/67375/WNG-886QCNVB-1 istex:94E4841B2AA4A6EEBDA30B0904FA5391AD81CDE3 ArticleID:SAPM12033 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0022-2526 1467-9590
DOI:	10.1111/sapm.12033