The Convergence of the Newton Iteration

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.It is required that there only exist one order derivate but not two order derivate for the function f(x) to discriminate the convergence of the Newton iteration in the theorem.The ruslts are tested and verified by the numerical examples.