矩阵方程A^TXA=B的反中心对称解及其最佳逼近  

Anti-centro-symetric Solution of the Matrix Equation A^TXA=B and Its Optimal Approximation

作　　者：巫晓宁[1] 邓继恩[1] 

机构地区：[1]河南理工大学数学与信息学院,河南焦作454003

出　　处：《吉林师范大学学报（自然科学版）》2011年第3期30-33,共4页Journal of Jilin Normal University:Natural Science Edition

基　　金：河南省基础与前沿研究计划项目(102300410233)

摘　　要：随着应用的推动,矩阵反问题的研究已经取得了许多进展.反中心对称矩阵在信息论,线性系统理论,线性估计系统理论等领域中有实际应用,而关于反中心对称矩阵的研究,国内外学者已在各个方面取得了突破,其多数方法为广义奇异分解与标准相关分解,详见[1-10].笔者利用矩阵对的商奇异值分解,得到矩阵方程ATXA=B的反中心对称解的充要条件及解的表达式,并研究了最佳逼近问题,给出了该问题有解的充要条件和解的表达式,最后给出了算法.With the application of the promotion, a lot of progress on the matrices has been made.Anti-centro-symetrie matrices have practical applications in information theory and other areas. Scholars havemade a breakthrough of the anti-eentro-symetric matrices on the research, and the methods applied are usually the generalized singular value decompositionand the canonical correlation decomposition, see[ 1-10]. By using the quotient singular value decomposi- tion of matrices this paper derives the necessary and sufficient conditions about the Anti-ceentro-symetric solution of the Matrix Equation ArXA = B and its expression. Its optimal approximation is also discussed, and the necessary and sufficient conditions about this problem is derived. The numerical algorithm is provided at last.

关 键 词：反中心对称矩阵 商奇异值分解 最佳逼近 

分 类 号：O224[理学—运筹学与控制论]