IMPROVED CONVERGENCE FOR KING-WERNER-TYPE DERIVATIVE FREE METHODS

Abstract

We present an improved semilocal and local convergence analysis of some efficient King-Werner-type methods of order $1+\sqrt{2}$ free of derivatives in a Banach space setting using our new idea of restricted convergence domains. In particular, a more precise convergence domain is determined containing the iterates than in earlier studies leading to: smaller Lipschitz constants, larger radii of convergence and tighter error bounds on the distances involved. Numerical examples are presented to illustrate the theoretical results.