New unifying convergence criteria for Newton-like methods

• Autorzy: Ioannis K. Argyros
• Języki publikacji: EN

Abstrakty

EN

We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence radius.

Kategorie tematyczne

• 49M15: Newton-type methods
• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 65N35: Spectral, collocation and related methods
• 65G99: None of the above, but in this section
• 65J15: Equations with nonlinear operators (do not use )
• 65B05: Extrapolation to the limit, deferred corrections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2002
• Tom: 29
• Numer: 3
• Strony: 359-369

Daty

wydano

2002

Twórcy

autor

Ioannis K. Argyros

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

Identyfikatory

DOI

10.4064/am29-3-7