Relaxing convergence conditions for Newton's method

[摘要] The classical Kantorovich theorem on Newton's method assumes that the first derivative of the operator involved satisfies a Lipschitz condition parallel to Gamma 0[F'(x) - F' (y)]parallel to less than or equal to L parallel to x - y parallel to. In this paper, we weaken this condition, assuming that parallel to Gamma(0)[F'(x) - F'(x(0))]parallel to less than or equal to omega(parallel to x - x(0)parallel to) for a given point x(0). (C) 2000 Academic Press.

[发布日期] 2000-09-15

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