论文信息 - Third-order iterative methods for operators with bounded second derivative

Third-order iterative methods for operators with bounded second derivative

Abstract We analyse the classical third-order methods (Chebyshev, Halley, super-Halley) to solve a nonlnnear 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.

José M. Gutiérrez | J. M. Gutiérrez | M. A. Hernández | Migual A. Hernández | J. Gutiérrez

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