On the Halley method in Banach spaces
Volume 39 / 2012
Applicationes Mathematicae 39 (2012), 243-255
MSC: 65H10, 65J15, 65G99, 47H17, 47J05, 49M15.
DOI: 10.4064/am39-2-9
Abstract
We provide a semilocal convergence analysis for Halley's method using convex majorants in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our results reduce and improve earlier ones in special cases.
