ArticleOriginal scientific text
Title
A new Kantorovich-type theorem for Newton's method
Authors 1
Affiliations
- Cameron University, Department of Mathematics, Lawton, Oklahoma 73505, U.S.A.
Abstract
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.
Keywords
Newton's method, Lipschitz-Hölder condition, Kantorovich hypothesis, Banach space
Bibliography
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- L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.
Pages:
151-157
Main language of publication
English
Received
1998-06-19
Published
1999
Exact and natural sciences