科研之友
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摘要
In this paper, we consider the matrix equation AXA(H) + CYCH = F, where A, C and F are given matrices with appropriate sizes and [X, Y] is an unknown Hermitian and generalized skew-Hamiltonian matrix pair. Based on matrix differential calculus and projection theorem in inner product spaces, we exploit the best approximate solution [(X) over cap, (Y) over cap] in the set S to a given matrix pair [X*, Y*], where S signifies the least-squares Hermitian and generalized skew-Hamiltonian solution set of the matrix equation AXA(H) + CYCH = F. The analytical expression of the best approximate solution is presented by applying the canonical correlation decomposition and the generalized singular value decomposition. Finally, a numerical algorithm and an illustrated example are given.
