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Third-order iterative methods for operators with bounded second derivative

✍ Scribed by JoséM. Gutiérrez; Miguel A. Hernández

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 591 KB
Volume: 82
Category: Article
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(97)00076-9

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✦ Synopsis

We analyse the classical third-order methods (Chebyshev, Halley, super-Halley) to solve a nonlinear equation F(x)= 0, where F is an operator defined between two Banach spaces. Until now the convergence of these methods is established assuming that the second derivative F" satisfies a Lipschitz condition. In this paper we prove, by using recurrence relations, the convergence of these and other third-order methods just assuming F" is bounded. We show examples where our conditions are fulfilled and the classical ones fail.

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