The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation

Journal of Applied Mathematics and Computing - Tập 27 - Trang 97-106 - 2008
Lei Yu1, Kaiyuan Zhang2, Zhongke Shi1
1College of Automation, Northwestern Polytechnical University, Xi’an, China
2Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, China

Tóm tắt

This paper discusses the anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation. By the generalized singular value decomposition of the matrices, the necessary and sufficient conditions for the solvability of the matrix equation and the general form of the anti-symmetric ortho-symmetric solution are given. In addition, the existence and uniqueness of the optimal approximation are proved. Numerical methods of the optimal approximation to a given matrix and numerical experiments are described.

Tài liệu tham khảo

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