A modification of the classic conditions of Newton-Kantorovich for Newton's method
We study the semilocal convergence of Newton's method in Banach spaces under a modification of the classic conditions of Kantorovich, which leads to a generalization of Kantorovich's theory. We illustrate this study with two Hammerstein integral equations of the second kind, where the classic conditions of Kantorovich cannot be applied, but our modification of them can. (C) 2012 Elsevier Ltd. All rights reserved.
newton's method semilocal convergence hammerstein integral equation kantorovich's technique majorizing sequence a priori error estimates