预条件平方Smith法求解连续Lyapunov方程  

A Preconditioned Squared Smith Method for Continuous-Time Lyapunov Equations

作　　者：蔡兆克 鲍亮[1] 初鲁 

机构地区：[1]华东理工大学数学系,上海200237

出　　处：《华东理工大学学报（自然科学版）》2016年第6期881-886,共6页Journal of East China University of Science and Technology

基　　金：中央高校基本科研业务费专项资金

摘　　要：探讨了如何数值求解连续时间的Lyapunov矩阵方程AX+XA^T+BB^T=0,给出了一种预条件的平方Smith算法,该算法首先利用交替方向隐式法即ADI法处理连续Lyapunov方程,构造出含ADI参数的对称Stein方程;然后利用平方Smith法迭代产生Krylov子空间中的低秩逼近形式。得到一些数值实验,这些例子表明预条件平方Smith法是非常有效的。This paper proposes a preconditioned squared Smith algorithm to solve the continuous-time Lyapunov matrix equations AX＋XA^T ＋ BB^T= 0 numerically. The method first uses the alternating directional implicit （ADI） method and transforms the original equations to the equivalent symmetric Stein matrix equations with some ADI parameters. Then we adopt the squared Smith algorithm to seek solutions of the Stein equations by generating the squared Smith iterations in some low-rank forms with the Krylov subspaces. And we give some numerical experiments to show the efficiency of this algorithm finally.

关 键 词：连续Lyapunov方程 预条件 平方Smith算法 ADI Krylov空间 

分 类 号：O242.2[理学—计算数学]