求解3×3对称鞍点问题的一种简化算法

A Simplified Algorithm for Solving 3×3 Symmetric Saddle Point Problem

为了有效提高对称鞍点问题的求解效率,将2×2块的对称鞍点问题转化为了3×3块的对称鞍点问题来求解.本文改进了基于3×3块鞍点问题提出的中心预处理的Uzawa-Low方法,得到了其简化格式.最后将算法简化格式与中心预处理的Uzawa-Low方法进行了数值实验,实验结果表明本文中的简化算法形式优于中心预处理的Uzawa-Low方法,即对对称鞍点问题的处理更为高效.

In order to effectively improve the efficiency of solving the symmetric saddle point problem,we could transform the symmetric saddle point problem of two-order block into the symmetric saddle point problem of three-order block.In this paper,the Uzawa-Low method with central preprocessing based on the saddle point problem of three-order block is improved,and the simplified one of this algorithm is obtained.Finally,the simplified algorithm and Uzawa-Low method with centered preconditioned are numerically tested.The experimental results show that the new algorithm is superior to centered preconditioned Uzawa-Low method,which means it is more efficient to deal with symmetric saddle point problems.