General convergence of the methods from Chebyshev-Halley family

Abstract

In this paper we study the Chebyshev-Halley family (which contains, as particular cases, the Chebyshev method, Halley method, super-Halley method and the C-method). For Chebyshev and super-Halley methods we give a global theorem of convergence. In the end of the paper we study the basins of attraction of the roots of a polynomial with real coefficients. They are obtained when we apply to that polynomial the methods from the Chebyshev-Halley family methods.

Keywords

• Chebyshev-Halley family of iterative methods
• basin of attraction
• fixed point
• periodic point
• attracting periodic point