Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646025 | Applied Numerical Mathematics | 2009 | 13 Pages |
Abstract
Assuming that the first derivative of an operator satisfies the Lipschitz condition, a Kantorovich-type convergence criterion for inexact Newton methods is established, which includes the well-known Kantorovich's theorem as a special case. Comparisons and a numerical example are presented to illustrate that our results obtained in the present paper improve and extend some recent results in [X.P. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math. 25 (2007) 231–242; W.P. Shen, C. Li, Convergence criterion of inexact methods for operators with Hölder continuous derivatives, Taiwan. J. Math. 12 (2008) 1865–1882].
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