A modified Chebyshev’s iterative method with at least sixth order of convergence

摘要

This paper is devoted to the construction and analysis of a high order variant of the classical Chebyshev method. The method has order of convergence at least six for simple roots. The extension to system of equations and its semilocal convergence for nonlinear equations are presented. Finally, an application to well-known algebraic Riccati equation is considered.