Abstract
We present a local convergence analysis of a family of third
order methods for approximating a locally unique solution of nonlinear
equations in a Banach space setting. Recently, the semilocal convergence
analysis of this method was studied by Chun, Stanic ˘ a and Neta in [10]. ˘
These authors extended earlier results by Kou, Li [17] and others [8, ?, 11,
13, 14]. The convergence analysis is based on hypotheses up to the second
Frechet derivative of the operator involved. This work further extends the ´
results of [10] and provides computable convergence ball and computable
error bounds under hypotheses only up to the first Frechet derivative.
I.K. Argyros, S.K. Khattri. (2014) Local convergence for a family of third order methods in Banach spaces, Punjab University Journal of Mathematics, Volume 46, Issue 2.
-
Views
563 -
Downloads
60
Article Details
Volume
Issue
Type
Language
