Kantorovich theorem was extended to variational inequalities by which the convergence of Newton iteration,the existence and uniqueness of the solution of the problem can be tested via computational conditions at the i...Kantorovich theorem was extended to variational inequalities by which the convergence of Newton iteration,the existence and uniqueness of the solution of the problem can be tested via computational conditions at the initial point.展开更多
The convergence criterion of Newton’s method to find the zeros of a map f from a Lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical Lipschitz condition, and ...The convergence criterion of Newton’s method to find the zeros of a map f from a Lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical Lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of f are estimated. Owren and Welfert (2000) stated that if the initial point is close sufficiently to a zero of f, then Newton’s method on Lie group converges to the zero; while this paper provides a Kantorovich’s criterion for the convergence of Newton’s method, not requiring the existence of a zero as a priori.展开更多
文摘Kantorovich theorem was extended to variational inequalities by which the convergence of Newton iteration,the existence and uniqueness of the solution of the problem can be tested via computational conditions at the initial point.
基金Project supported by the National Natural Science Foundation of China (No. 10271025)the Program for New Century Excellent Talents in University of China
文摘The convergence criterion of Newton’s method to find the zeros of a map f from a Lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical Lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of f are estimated. Owren and Welfert (2000) stated that if the initial point is close sufficiently to a zero of f, then Newton’s method on Lie group converges to the zero; while this paper provides a Kantorovich’s criterion for the convergence of Newton’s method, not requiring the existence of a zero as a priori.
