Convergence of Halley’s method for operators with the bounded second Fréchet-derivative in Banach spaces

Journal of inequalities and applications

Ioannis K Argyros¹ 

关键词: Halley’s method;    Banach space;    semi-local convergence;    Fréchet-derivative;    convergence ball;   

DOI  :  10.1186/1029-242X-2013-260

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we present a semi-local convergence analysis of Halley’s method for approximating a locally unique solution of a nonlinear equation in a Banach space setting, where we assume that the second Fréchet-derivative is bounded. Numerical examples are used to show that the new convergence criteria can provide better information than those provided by the convergence criteria developed earlier. MSC:65G99, 65J15, 65H10, 47H17, 49M15.

【 授权许可】

CC BY