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New Kantorovich-Type Conditions for Halley's Method

✍ Scribed by J. A. Ezquerro; M. A. Hernández

Publisher
John Wiley and Sons
Year
2005
Weight
130 KB
Volume
2
Category
Article
ISSN
1611-8170

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✦ Synopsis

Two new semilocal convergence results of Newton-Kantorovich type are presented for the Halley method, where the usual convergence conditions, which appears in the literature, are relaxed. In one of them, it is supposed that the second derivative F of a nonlinear operator F satisfies F (x0) ≤ α instead of F (x) ≤ M , for all x in a subset of the domain of F , where α and M are positive real constants. In the other one fewer convergence conditions are required than all the existing ones until now.

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