Local convergence of Newton-Steffensen type iteration under Hlder condition of the first order derivative;

This paper presents a new method for solving Kepler equation by Steffensen iteration method, which successfully conquers the disadvantages of low convergence speed in normal Fixed-Point iteration method , and at the same time avoids repeatedly derivative calculation and relatively complicated iteration structure in Newton iteration method, so it has high precision and fast convergence rate .

Thus,we get two new Newton-type iterative method.

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.