LOCAL CONVERGENCE OF SIXTH-ORDER NEWTON-LIKE METHODS BASED ON STOLARSKY AND GINI MEANS
IOANNIS K. ARGYROS
Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
SANTHOSH GEORGE *
Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, India
SHOBHA M. ERAPPA
Department of Mathematics, MIT Manipal, 576104, India
*Author to whom correspondence should be addressed.
Abstract
Stolarsky-Gini means have been used in connection to a sixth order Newton-like method to compute solutions of nonlinear equations defined on the real line [1,2,3,4]. The local convergence was shown using Taylor expansions and conditions reaching at least until the seventh derivative, although only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. In the present article we show convergence based only on the first derivative. The numerical examples justify the theoretical results.
Keywords: Newton-like method, local convergence, Stolarsky means, Gini means, efficiency index