LOW RANK APPROXIMATION SOLUTION OF A CLASS OF GENERALIZED LYAPUNOV EQUATION  

作　　者：Xuefeng Duan Zhuling Jiang Anping Liao 

机构地区：[1]College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, P.R. China [2]Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Teehnology, Guilin 541004, P.R. China [3]College of Mathematics and Econometrics, Hunan University, Changsha 410082, P.R. China

出　　处：《Journal of Computational Mathematics》2016年第4期407-420,共14页计算数学（英文）

摘　　要：In this paper, we consider the low rank approximation solution of a generalized Lya- punov equation which arises in the bilinear model reduction. By using the variation prin- ciple, the low rank approximation solution problem is transformed into an unconstrained optimization problem, and then we use the nonlinear conjugate gradient method with ex- act line search to solve the equivalent unconstrained optimization problem. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.In this paper, we consider the low rank approximation solution of a generalized Lya- punov equation which arises in the bilinear model reduction. By using the variation prin- ciple, the low rank approximation solution problem is transformed into an unconstrained optimization problem, and then we use the nonlinear conjugate gradient method with ex- act line search to solve the equivalent unconstrained optimization problem. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

关 键 词：Generalized Lyapunov equation Bilinear model reduction Low rank approxi-mation solution Numerical method. 

分 类 号：O224[理学—运筹学与控制论] TP13[理学—数学]