Based on the analysis of the zero set characteristics of the nonlinear polynomial mapping homotopy function, a homotopy iteration method with an improved homotopy tracking scheme is proposed in this paper, and the feasibility and reliability of the homotopy iteration method for solving nonlinear polynomial systems is proved.

And we will give the iterative methods for computing the weighted α β generalized inverse and the sufficient and necessary conditions are obtained.

Without any functional expansions, accurate orientational distribution functions are obtained by using a newly iterative method to solve the equation of equilibrium state.

By means of iterative method,the existence and convergence of the solutions are showed in case Ais invertible.

In respect to the shortest path problem of the weighed direct graph,the iterative method of minimum algebra is established.

A solution of a sort special matrix equation by iteration method;

In this paper we present a new iteration method with high accuracy for solving nonlinear equations, This method has not only 5-order convergence but also avoids the operation of derivatives.

The existence and uniqueness of the solution to the equation x=A(x,…,x) is studied in weaker condition by using the cones theory and iteration method.