Convergence Conditions for the Secant Method

We 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 d...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Argyros,Ioannis K, Hilout,Saïd
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2010
Materias:	Secant method Banach space majorizing sequence divided difference Fréchet-derivative
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100014
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0719-06462010000100014
record_format	dspace
spelling	oai:scielo:S0719-064620100001000142018-10-08Convergence Conditions for the Secant MethodArgyros,Ioannis KHilout,Saïd Secant method Banach space majorizing sequence divided difference Fréchet-derivative We 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.1 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100014en10.4067/S0719-06462010000100014
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Secant method Banach space majorizing sequence divided difference Fréchet-derivative
spellingShingle	Secant method Banach space majorizing sequence divided difference Fréchet-derivative Argyros,Ioannis K Hilout,Saïd Convergence Conditions for the Secant Method
description	We 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.
author	Argyros,Ioannis K Hilout,Saïd
author_facet	Argyros,Ioannis K Hilout,Saïd
author_sort	Argyros,Ioannis K
title	Convergence Conditions for the Secant Method
title_short	Convergence Conditions for the Secant Method
title_full	Convergence Conditions for the Secant Method
title_fullStr	Convergence Conditions for the Secant Method
title_full_unstemmed	Convergence Conditions for the Secant Method
title_sort	convergence conditions for the secant method
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2010
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100014
work_keys_str_mv	AT argyrosioannisk convergenceconditionsforthesecantmethod AT hiloutsaid convergenceconditionsforthesecantmethod
_version_	1714206763991957504

Convergence Conditions for the Secant Method

Ejemplares similares