Some Iteration Methods with High-Order Convergence for Nonlinear Equations

Abstract

In this paper the iteration methods with high-order convergence for nonlinear equations are studied. It is shown that all the iteration methods with third-order convergence are equivalent to the standard Tchebyshev method. The acceleration of the convergence of the Newton method is also considered. New iteration methods on the procedure discussed above are proposed. Comparison between different iteration methods is given by test examples.