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.

In this paper,some new theorems of convergence of the Newton iteration and Newton descent method in larger convergence domain are introduced,and the expressions of error estimate about these two iterations are presented.

With reconstructions and extensions towards classical principalagent theory, this paper brings forward obendeavor theorem, validates moral hazard with hidden action, and discovers coordinating effect of the level of endeavor towards endeavor effect index through calculating longterm endeavor of the entrepreneur by the method of Newton iteration and graphics.

Newton iteration method for solving the system of no nlinear equations is improved, restriction on its iteration function is relaxed, the convergence of the improved iteration algorithm is proved strictly, and the theoretical basis for designing cheaper and faster iteration methods is supplie d.

This paper describs a corrector Newton iteration method for solving equation with one unknown.

Instead of the linearization of expression of thermal radiation on free surface,start at Galerkin finite element method,convert the calculation problem of the temperature field into a calculation of nonlinear equations,and then calculate the temperature by Newton iteration method.

An generalized Newton iterative method for extracting the roots of a category equation;

Newton iterative method based on Hénon chaos mapping for seeking the positional forward solution of parallel mechanism

Seydel s method is taken as first step to make prediction,and then Newton iterative method to make correction along the direction which is orthogonal to that found in the first step.