New conditions for the convergence of newton-kantorovich method and some their applications

The method of Newton-Kantorovich and its analogs are considered in the paper aiming at the establishment of convergence conditions and a priori estimations for approximations of Newton-Kantorovich under Wertgame's conditions. During the investigation the new variant of the majorant method for the convergence investigation of Newton-Kantorovich processes and the general theory of Banakh spaces have been used. As a result the new modification of the majorant method for the investigation of Newton-Kantorovich method and its analogs has been siggested. New effective estimations of the methods considered have been obtained. The new convergence conditions for Newton-Kantorovich method have been obtained as well as estimations for the speed of this convergence, estimations convinient for the numerical solution of concrete non-linear equations. The paper results may find their field of application in theory of approximate methodsAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio