A new Kantorovich-type theorem for Newton's method

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

Abstrakty

EN

A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.

Słowa kluczowe

EN

Newton's method; Lipschitz-Hölder condition; Kantorovich hypothesis; Banach space

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1999
• Tom: 26
• Numer: 2
• Strony: 151-157

Daty

wydano

1999

otrzymano

1998-06-19

Twórcy

autor

Ioannis K. Argyros

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

Bibliografia

• [1] I. K. Argyros, Newton-like methods under mild differentiability conditions with error analysis, Bull. Austral. Math. Soc. 37 (1988), 131-147.
• [2] I. K. Argyros and F. Szidarovszky, The Theory and Applications of Iteration Methods, C.R.C. Press, Boca Raton, Fla., 1993.
• [3] J. M. Gutiérrez, A new semilocal convergence theorem for Newton's method, J. Comput. Appl. Math. 79 (1997), 131-145.
• [4] J. M. Gutiérrez, M. A. Hernández, and M. A. Salanova, Accessibility of solutions by Newton's method, Internat. J. Comput. Math. 57 (1995), 239-247.
• [5] Z. Huang, A note on the Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993), 211-217.
• [6] L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.