求解双鞍点问题的一个新预处理子

A New Preconditioner for Solving the Double Saddle Point Problem

对双鞍点问题系数矩阵的子块引入一个合适的对称正定矩阵(不含参数),可以有效避免参数选取困难.基于这种思想,提出了一种新的迭代方法和预处理子用来求解双鞍点问题,给出该迭代方法的收敛条件,并对预处理系统的系数矩阵进行谱分析,数值实验验证了该预处理子的有效性.

By introducing a suitable symmetric positive definite matrix(without parameters)into the sub blocks of the coefficient matrix of the double saddle point problem,the difficulty of parameter selection can be effectively avoided.Based on this idea,in this paper,a new iterative method and preconditioner are proposed to solve the double saddle point problem.The convergence conditions of the iterative method are given,and the spectral analysis of the preconditioned coefficient matrix is performed.Numerical experiments have verified the effectiveness of this preconditioner.