广义鞍点问题的块三角预条件子

本文对Golub和Yuan(2002)中给出的ST分解推广到广义鞍点问题上,给出了三种块预条件子,并重点分析了其中两种预条件子应用到广义鞍点问题上所得到的对称正定阵,得出了其一般的性质并重点研究了预处理矩阵条件数的上界,最后给出了数值算例.

BLOCK TRIANGULAR PRECONDITIONERS FOR GENERALIZED SADDLE POINT PROBLEMS

In this paper, we extend the ST decomposition which is given by Golub and Yuan (2002) to the generalized saddle point problem and present three block triangular preconditioners. Then we take two of them and apply them to the generalized saddle point problem. The two preconditioned systems are symmetric and positive definite. Then we deduce the general properties and the upper bound of the condition number of the two preconditioned systems one by one. Finally, numerical computation based on a particular linear system is given, which clearly shows the advantage.