Local convergence of general Steffensen type methods

We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence order of the classical Steffensen method. The convergence order of our method is greater or equal to the number of the controlled nodes used in the Lagrange-type inverse...

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Bibliographic Details
Published inJournal of numerical analysis and approximation theory Vol. 33; no. 1
Main Author Ion Păvăloiu
Format Journal Article
LanguageEnglish
Published Publishing House of the Romanian Academy 01.02.2004
Subjects
nonlinear scalar equations
Steffensen type method
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Summary:We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence order of the classical Steffensen method. The convergence order of our method is greater or equal to the number of the controlled nodes used in the Lagrange-type inverse interpolation, which, in its turn, is substantially higher than the convergence orders of the Lagrange type inverse interpolation with uncontrolled nodes (since their convergence order is at most \(2\)).
ISSN:2457-6794
2501-059X
DOI:10.33993/jnaat331-762