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Zbl 1027.65078
Wang, Xinghua; Li, Chong
Convergence of Newton's method and uniqueness of the solution of equations in Banach spaces. II.
(English)
[J] Acta Math. Sin., Engl. Ser. 19, No.2, 405-412 (2003). ISSN 1439-8516; ISSN 1439-7617/e

The authors continue their work on the Newton-Kantorowitsch method for solving nonlinear equations in a Banach space. Convergence and uniqueness results are studied under the assumption that the operator's derivative fulfills a so-called radius or center Lipschitz condition with the weak $L$ average. Part I of this work has been published by {\it X. Wang} [IMA J. Numer. Anal. 20, No. 1, 123-134 (2000; Zbl 0942.65057)]. The reader should also consult {\it X. Wang, C. Li,}\/ and {\it M.-J. Lai} [BIT 42, 206-213 (2002; Zbl 0998.65057)].
[Etienne Emmrich (Berlin)]
MSC 2000:
*65J15 Equations with nonlinear operators (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)

Keywords: nonlinear equation; Banach space; Newton-type method; convergence

Citations: Zbl 0942.65057; Zbl 0998.65057

Cited in: Zbl 1158.65325

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