Volume no :2, Issue no: 2, November (2009)

ON THE CONVERGENCE OF A JARRATT-TYPE METHOD USING RECURRENT FUNCTIONS

Author's: Ioannis K. Argyros and Saïd Hilout
Pages: [121] - [144]
Received Date: April 16, 2009; Revised October 20, 2009
Submitted by: Jinhai Chen

Abstract

We use a fourth order Jarratt-type method to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Using our new idea of recurrent functions, we provide new sufficient convergence conditions, and finer error bounds than before [1]-[10].

Keywords

Jarratt method, Newton-type methods, Banach space, Fréchet-derivative, majorizing sequence, recurrent functions.