LOCAL CONVERGENCE OF A HANSEN-PATRICK-LIKE FAMILY OF OPTIMAL FOURTH ORDER METHODSIOANNIS K. ARGYROS, SANTHOSH GEORGE (pp. 32-39)
We present a local convergence analysis of an optimal fourth order Hansen-Patricklike family of methods in order to approximate a solution of a nonlinear equation. Earlier studies use hypotheses involving derivatives up to the third order to show convergence although only the first derivative appears in these methods. In the present study we use only hypotheses on the first derivative. We also provide computable error bounds on the distances involved based on Lipschitz constants. This way we expand the applicability of these methods. Numerical examples are also given in this study.
Hansen-Patrick-like family, optimal method, local convergence.