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 | References | Similar Articles | Additional Information

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

DOI:
https://doi.org/10.1090/S0025-5718-99-00999-0

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