HIGH CONVERGENCE ORDER SOLVERS IN BANACH SPACE

IOANNIS K.  ARGYROS; SANTHOSH  GEORGE

HIGH CONVERGENCE ORDER SOLVERS IN BANACH SPACE

Authors

IOANNIS K. ARGYROS Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
SANTHOSH GEORGE Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025

Keywords:

Banach space, Newton-type, local convergence, Fr\'echet derivative

Abstract

The local convergence of an eighth order solver is established using only the first derivative for Banach space valued operators. Earlier studies have used up to the ninth order derivatives, which limit the applicability of the solver. The results are tested using numerical experiments.