Broyden method for nonlinear equation in several variables is presented, its local and semilocal convergence properties are discussed, and its superlinear convergence rate is estimated.

This dissertation mainly study the theoretic analysis of solving nonlinear equations f(x) = 0 in Banach space, especially on the local and semi-local convergenceof Newton s method, inexact Newton method and Newton-like method.

The semilocal convergence of the general quasi-Newton method for nonlinear complementarity problems is studied in this paper and the Mysovskii type convergence theorem is obtained.

The semilocal convergence properties of a variant of Chebyshev iteration method for nonlinear operator equations were studied under the hypothesis that the first derivative satisfied some mild differentiability conditions.

The proof of the local convergence of the semi-implicit Euler method for a linear stochastic differential delay equation;

Under the hypothesis that the first order derivative of a nonlinear operator f satisfied Hlder continuous condition around the zero of f(x),a local convergence theorem for this method was established in Banach spaces,and the local convergence with order 1+p was presented.

We prove the local convergence pro-perties of the algorithm assoicated with the general form of linesearch.

In this paper the local convergence properties of the filter trust region algorithm is discussed.

The algorithm generates detectors with an r-contiguous-bits unchanged rule(r-CBUR)and a p-receptor editing to search in a wide feature space and try to avoid local convergences.

The local convergence properties of the filter trust region algorithm was discussed.