Convergence Conditions for the Secant Method

dc.creatorArgyros,Ioannis K
dc.creatorHilout,Sa<img width=10 height=18 src="http:/fbpe/img/cubo/v12n1/img40.jpg">d
dc.date2010-01-01
dc.date.accessioned2017-03-07T16:37:33Z
dc.date.available2017-03-07T16:37:33Z
dc.identifierhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100014
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/404781
dc.descriptionWe provide new sufficient convergence conditions for the convergence of the Secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions are violated. Numerical examples are also provided in this study.
dc.formattext/html
dc.languageen
dc.publisherUniversidad de La Frontera. Departamento de Matemática y Estadística
dc.publisherUniversidade Federal de Pernambuco. Departamento de Matemática
dc.sourceCubo (Temuco) v.12 n.1 2010
dc.subjectSecant method
dc.subjectBanach space
dc.subjectmajorizing sequence
dc.subjectdivided difference
dc.subjectFréchet-derivative
dc.titleConvergence Conditions for the Secant Method
dc.typeArtículos de revistas


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