代序

This paper points out that if a sequence of Jacobian approximation satisfies the bounded deterioration, the sequence generated from the quasi& Newton methods is no better than linear convergence.

本文指出当Jacobian近似满足有界退化性质时，由拟牛顿算法得到的迭代序列最多是线性收敛的。

A new iterative scheme is introduced which is proved to be weakly convergent to zero point of maximal monotone operator A by using the techniques of Lyapunov functional, Qr operator and generalized projection operator, etc.

本文将引入新的迭代算法，并利用Lyapunov泛函，Qr算子与广义投影算子等技巧，证明了迭代序列弱收敛于极大单调算子A的零点的结论。

For a nonlinear system of ordinary differential equations, we construct an iterative sequence and prove that the sequence is bounded. Using the sequence, the approximate solution is obtained.

对于非线性微分方程组，构造了一个迭代序列，证明了迭代序列是有界的，利用迭代序列构造近似解的表达形式。