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| YiqinLIN,LiangBAO,YanhuaCAO,LipingZHOU |
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| (Department of Mathematics and Computational Science, Hunan University of Science and Engineering;Department of Mathematics, East China University of Science and Technology;Department of Mathematics, North China Electric Power University) |
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| Received:August 17, 2010Revised:January 26, 2011 |
| 基金项目:This work was supported by the National Natural Science Foundation of China (Nos. 10801048, 10926150, 11101149), the Natural Science Foundation of Hunan Province (No. 09JJ6014), the Key Program of the Scientific Research Foundation from Education Bureau of Hunan Province (No. 09A033), the Scientific Research Foundation of Education Bureau of Hunan Province for Outstanding Young Scholars in University (No. 10B038), the Science and Technology Planning Project of Hunan Province (No. 2010JT4042), the Young Core Teacher Foundation of Hunan Province in University, and the Fundamental Research Funds for the Central Universities. |
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| A direct method for solving projected generalized continuous-time Sylvester equations |
| Yiqin LIN,Liang BAO,Yanhua CAO,Liping ZHOU |
| (Department of Mathematics and Computational Science, Hunan University of Science and Engineering;Department of Mathematics, East China University of Science and Technology;Department of Mathematics, North China Electric Power University) |
| Abstract: |
| This article is devoted to the numerical solution of a projected generalized Sylvester equation with relatively small size. Such an equation arises in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. The algebraic formula of the solution of the projected generalized continuous-time Sylvester equation is presented. A direct method based on the generalized Schur factorization is proposed. Moreover, its low-rank version for problems with low-rank right-hand sides is also proposed. The computational cost of the direct method is estimated. Numerical simulation show that this direct method has high accuracy. |
| Key words: Projected generalized Sylvester equation Matrix pencil Generalized Schur factorization Spectral projection |
