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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Convergence of Newton's method
and inverse function theorem
in Banach space

Author: Wang Xinghua
Journal: Math. Comp. 68 (1999), 169-186
MSC (1991): Primary 65H10
MathSciNet review: 1489975
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Abstract: Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, a proper condition which makes Newton's method converge, and an exact estimate for the radius of the ball of the inverse function theorem are given in a Banach space. Also, the relevant results on premises of Kantorovich and Smale types are improved in this paper.

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Additional Information

Wang Xinghua
Affiliation: Department of Mathematics, Hangzhou University, Hangzhou 310028 China

Received by editor(s): March 12, 1997
Received by editor(s) in revised form: June 6, 1997
Additional Notes: Supported by the China State Major Key Project for Basic Research and the Zhejiang Provincial Natural Science Foundation.
Article copyright: © Copyright 1999 American Mathematical Society