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Volume 34, Issue 4
Low Rank Approximation Solution of a Class of Generalized Lyapunov Equation

Xuefeng Duan, Zhuling Jiang & Anping Liao

DOI: 10.4208/jcm.1601-m2015-0388

J. Comp. Math., 34 (2016), pp. 407-420.

Published online: 2016-08

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  • Abstract

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

  • Keywords

Generalized Lyapunov equation, Bilinear model reduction, Low rank approximation solution, Numerical method.

  • AMS Subject Headings

15A24, 65F30, 93A15.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

guidian520@126.com (Xuefeng Duan)

543274306@qq.com (Zhuling Jiang)

liaoap@hnu.edu.cn (Anping Liao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-407, author = {Duan , XuefengJiang , Zhuling and Liao , Anping}, title = {Low Rank Approximation Solution of a Class of Generalized Lyapunov Equation}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {4}, pages = {407--420}, abstract = {

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

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1601-m2015-0388}, url = {http://global-sci.org/intro/article_detail/jcm/9803.html} }
TY - JOUR T1 - Low Rank Approximation Solution of a Class of Generalized Lyapunov Equation AU - Duan , Xuefeng AU - Jiang , Zhuling AU - Liao , Anping JO - Journal of Computational Mathematics VL - 4 SP - 407 EP - 420 PY - 2016 DA - 2016/08 SN - 34 DO - http://doi.org/10.4208/jcm.1601-m2015-0388 UR - https://global-sci.org/intro/article_detail/jcm/9803.html KW - Generalized Lyapunov equation, Bilinear model reduction, Low rank approximation solution, Numerical method. AB -

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

Duan , XuefengJiang , Zhuling and Liao , Anping. (2016). Low Rank Approximation Solution of a Class of Generalized Lyapunov Equation. Journal of Computational Mathematics. 34 (4). 407-420. doi:10.4208/jcm.1601-m2015-0388
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