ON THE SEMILOCAL CONVERGENCE OF ULM'S METHOD

IOANNIS K.  ARGYROS; SAÏD  HILOUT

ON THE SEMILOCAL CONVERGENCE OF ULM'S METHOD

Authors

IOANNIS K. ARGYROS Cameron university, Department of Mathematical Sciences, Lawton, OK 73505, USA
SAÏD HILOUT Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France

Keywords:

Ulm’s method, Newton’s method, Banach space, Recurrence relations, Semilocal convergence, Fréchet derivative

Abstract

We provide sufficient convergence conditions for the semilocal convergence of Ulm's method [9] to a locally unique solution of an equation in a Banach space setting. Our results compare favorably to recent ones by Ezquerro and Hernández [3] which have improved earlier ones [4], [6]-[10], since under the same computational cost we provide: larger convergence domain; finer error bounds on the distances involved, and an at least as precise information on the location of the solution.