On the convergence of Newton's method under ω*-conditioned second derivative

• Autorzy: Ioannis K. Argyros , Saïd Hilout
• Języki publikacji: EN

Abstrakty

EN

We provide a new semilocal result for the quadratic convergence of Newton's method under ω*-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using ω-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.

Kategorie tematyczne

• 49M15: Newton-type methods
• 65G99: None of the above, but in this section
• 65J15: Equations with nonlinear operators (do not use )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2011
• Tom: 38
• Numer: 3
• Strony: 341-355

Daty

wydano

2011

Twórcy

autor

Ioannis K. Argyros

• Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, U.S.A.

autor

Saïd Hilout

• Laboratoire de Mathématiques et Applications, Université de Poitiers, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France

Identyfikatory

DOI

10.4064/am38-3-5