Improved ball convergence of Newton's method under general conditions

• Autorzy: Ioannis K. Argyros , Hongmin Ren
• Języki publikacji: EN

Abstrakty

EN

We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of the solution.

Kategorie tematyczne

• 49M15: Newton-type methods
• 65K10: Optimization and variational techniques
• 65G99: None of the above, but in this section
• 90C30: Nonlinear programming

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2012
• Tom: 39
• Numer: 3
• Strony: 365-375

Daty

wydano

2012

Twórcy

autor

Ioannis K. Argyros

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

autor

Hongmin Ren

• College of Information and Electronics, Hangzhou Polytechnic, Hangzhou 311402, Zhejiang, P.R. China

Identyfikatory

DOI

10.4064/am39-3-9