Convergence conditions for the secant method

dc.creator	Argyros, Ioannis K.
dc.creator	Hilout, Saïd
dc.date	2010-03-01
dc.identifier	https://revistas.ufro.cl/ojs/index.php/cubo/article/view/1434
dc.identifier	10.4067/S0719-06462010000100014
dc.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.	en-US
dc.format	application/pdf
dc.language	eng
dc.publisher	Universidad de La Frontera. Temuco, Chile.	en-US
dc.relation	https://revistas.ufro.cl/ojs/index.php/cubo/article/view/1434/1290
dc.source	CUBO, A Mathematical Journal; Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal; 161–174	en-US
dc.source	CUBO, A Mathematical Journal; Vol. 12 Núm. 1 (2010): CUBO, A Mathematical Journal; 161–174	es-ES
dc.source	0719-0646
dc.source	0716-7776
dc.subject	Secant method	en-US
dc.subject	Banach space	en-US
dc.subject	majorizing sequence	en-US
dc.subject	divided difference	en-US
dc.subject	Fréchet–derivative	en-US
dc.title	Convergence conditions for the secant method	en-US
dc.type	info:eu-repo/semantics/article
dc.type	info:eu-repo/semantics/publishedVersion