Local convergence for composite Chebyshev-type methods

Abstract

We replace Chebyshev's method for solving equations requiring the second derivative by a Chebyshev-type second derivative free method. The local convergence analysis of the new method is provided using hypotheses only on the first derivative in contrast to the Chebyshev method using hypotheses on the second derivative. This way we extend the applicability of the method. Numerical examples are also used to test the convergence criteria and to obtain error bounds and also the radius of convergence.