MINIMIZATION PROBLEM FOR SYMMETRIC ORTHOGONAL ANTI-SYMMETRIC MATRICES  

作　　者：Yuan Lei Anping Liao Lei Zhang 

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

出　　处：《Journal of Computational Mathematics》2007年第2期211-220,共10页计算数学（英文）

基　　金：The Project supported by Scientific Research Fund of Hunan Provincial Education Department,by National Natural Science Foundation of China (10171031);by Natural Science Fundation of Hunan Province (03JJY6028).

摘　　要：By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution ^-X, which is both a least-squares symmetric orthogonal anti-symmetric solu- tion of the matrix equation A^TXA = B and a best approximation to a given matrix X^＊. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution ^-X, which is both a least-squares symmetric orthogonal anti-symmetric solu- tion of the matrix equation A^TXA = B and a best approximation to a given matrix X^＊. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.

关 键 词：Symmetric orthogonal anti-symmetric matrix Generalized singular value decomposition Canonical correlation decomposition 

分 类 号：O241.6[理学—计算数学]