Least-Squares Solution with the Minimum-Norm for the Matrix Equation A^TXB+B^TX^TA = D and Its Applications  

作　　者：An-ping Liao Yuan Lei Xi-yan Hu 

机构地区：[1]Coilege of Mathematics and Econometrics, Hunan University, Changsha 410082, China [2]Department of Mathematics and Information Sciences, Changsha University, Changsha 410003, China

出　　处：《Acta Mathematicae Applicatae Sinica》2007年第2期269-280,共12页应用数学学报（英文版）

基　　金：Natural Science Fund of Hunan Province(No.03JJY6028);National Natural Science Foundation of China(No.10171032)

摘　　要：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.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.

关 键 词：Matrix equation minimum-norm solution generalized singular value decomposition canonical correlation decomposition 

分 类 号：O151.21[理学—数学] O241.6[理学—基础数学]