On the Generalized Halley Method for Solving Nonlinear Equations

Authors

G. Albeanu

Year

2008

Journal Paper

Algorithm

Generalized Halley Method

Source

ROMAI Journal

Abstract¶

Halley's method is a famous iteration method for solving nonlinear equations F (X) = 0. Some Kantorovich-like theorems have been given, including extensions for general spaces. Quasi-Halley methods were proposed too. This paper uses the generalized inverse approach in order to obtain a robust generalized Halley method.

Summary¶

Analyzes generalized Halley iterations for solving nonlinear equations, extending classical higher-order root-finding theory. The paper is mainly useful as a convergence reference for families of Newton-like methods.