On the gap between the semilocal convergence domains of two Newton methods

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

Abstrakty

EN

We answer a question posed by Cianciaruso and De Pascale: What is the exact size of the gap between the semilocal convergence domains of the Newton and the modified Newton method? In particular, is it possible to close it? Our answer is yes in some cases. Using some ideas of ours and more precise error estimates we provide a semilocal convergence analysis for both methods with the following advantages over earlier approaches: weaker hypotheses; finer error bounds on the distances involved, and at least as precise information on the location of the solution; and a smaller gap between the two methods.

Kategorie tematyczne

• 49M15: Newton-type methods
• 65G99: None of the above, but in this section
• 65H10: Systems of equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2007
• Tom: 34
• Numer: 2
• Strony: 193-204

Daty

wydano

2007

Twórcy

autor

Ioannis K. Argyros

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

Identyfikatory

DOI

10.4064/am34-2-4