Halley's method for operators with unbounded second derivative

doi:10.1016/j.apnum.2006.05.001

Applied Numerical Mathematics

Volume 57, Issue 3, March 2007, Pages 354-360

https://doi.org/10.1016/j.apnum.2006.05.001 Get rights and content

Abstract

A new semilocal convergence result of Newton–Kantorovich type for the Halley method is presented, where a new technique is provided to analyze the semilocal convergence. The usual convergence conditions are relaxed, since the second derivative $F^{″}$ of a nonlinear operator F satisfies $‖ F^{″} (x_{0}) ‖ ⩽ α$ instead of $‖ F^{″} (x) ‖ ⩽ M$ , for all x in a subset of the domain of F, where α and M are positive real constants.

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^☆: Preparation of this paper was partly supported by the Ministry of Education and Science of Spain (MTM 2005-30091).

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Halley's method for operators with unbounded second derivative☆

Abstract

Chem. Engrg. Sci.

Appl. Math. Comput.

Appl. Math. Comput.

J. Comput. Appl. Math.

The Halley method in Banach spaces and the Ptak error estimates

Rev. Acad. Cienc. Zaragoza (2)