Third-order iterative methods for operators with bounded second derivative

[摘要] 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.

[发布日期] 1997-09-15

[效力级别]  Proceedings Paper

[关键词] nonlinear equations in Banach spaces;third-order method;recurrence relations;convergence theorem