An efficient method based on the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition is presented to find the least-squares solution with the minimum-norm for t...An efficient method based on the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition is presented to find the least-squares solution with the minimum-norm for the matrix equation A^TXB＋B^TX^TA = D. Analytical solution to the matrix equation is also derived. Furthermore, we apply this result to determine the least-squares symmetric and sub-antisymmetric solution of the matrix equation C^TXC = D with minimum-norm. Finally, some numerical results are reported to support the theories established in this paper.展开更多
基金Natural Science Fund of Hunan Province(No.03JJY6028)National Natural Science Foundation of China(No.10171032)
文摘An efficient method based on the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition is presented to find the least-squares solution with the minimum-norm for the matrix equation A^TXB＋B^TX^TA = D. Analytical solution to the matrix equation is also derived. Furthermore, we apply this result to determine the least-squares symmetric and sub-antisymmetric solution of the matrix equation C^TXC = D with minimum-norm. Finally, some numerical results are reported to support the theories established in this paper.
