关键词: 鞍点问题, 迭代法, Ｕｚａｗａ－ＡＯＲ方法, 收敛性

Abstract:

Saddle point linear system is a symmetric and indefinite linear system，which comes from the optimization problem，the least sduare problem and so on. In practical applications，the system is usually large，and the coefficient matrix is sparse，so we should use the iterative method to solve the problem. Uzawa algorithm is an effective method for solving the saddle point problem，the algorithm is simple，but it is slow in convergence. In this paper, it is of great interest to develop an efficient iterative method for solving the saddle point problems.  Based on iterative scheme，we present a new Uzawa一AOP method and prove the convergence of the proposed method.  Actually，the new method can be considered as an inexact iteration method with the Uzawa as the outer iteration and the AOP as the inner iteration.  Numerical examples are used to illustrate the efficiency of the new iteration method.

Key words: saddle point problems, iterative method, Uzawa一AOP method, convergence