A modification of the classical Kantorovich conditions for Newton's method

[摘要] In the classical Kantorovich theorem on Newton's method it is assumed that the second Frechet derivative of the involved operator satisfies the condition parallel toF(x)parallel to less than or equal to K in an appropiate domain. In this paper we study a modification of this condition, assuming that parallel toF(x)parallel to less than or equal to omega(parallel tox parallel to), where omega is a continuous and non-decreasing real function. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-12-01

[关键词] iterative processes;Newton's method;Kantorovich conditions