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 inc...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 accurncv展开更多
Let M =（ABCD）（A and D are square） be a 2 × 2 block matrixgeneralized Schur complement of M. We give the representations and the group invertibility of M under each of the following conditions： （1） S = 0; ...Let M =（ABCD）（A and D are square） be a 2 × 2 block matrixgeneralized Schur complement of M. We give the representations and the group invertibility of M under each of the following conditions： （1） S = 0; （2） S is group invertible and CAπB = 0, where Aπ= I - AA#. And the second result generalizes a result of C. Bu et al. [Appl. Math. Comput., 2009, 215： 132-139].展开更多
基金supported by the National Natural Science Foundation of China(Nos.10801048,10926150,11101149)the Natural Science Foundation of Hunan Province(No.09JJ6014)+4 种基金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 Universitythe Fundamental Research Funds for the Central Universities
文摘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 accurncv
文摘Let M =（ABCD）（A and D are square） be a 2 × 2 block matrixgeneralized Schur complement of M. We give the representations and the group invertibility of M under each of the following conditions： （1） S = 0; （2） S is group invertible and CAπB = 0, where Aπ= I - AA#. And the second result generalizes a result of C. Bu et al. [Appl. Math. Comput., 2009, 215： 132-139].
