东北电力大学学报
東北電力大學學報
동북전력대학학보
JOURNAL OF NORTHEAST DIANLI UNIVERSITY
2014年
4期
80-85
,共6页
王小雪%程宏伟%杨琼琼%周硕
王小雪%程宏偉%楊瓊瓊%週碩
왕소설%정굉위%양경경%주석
广义反中心对称矩阵%子矩阵约束%反问题%最佳逼近
廣義反中心對稱矩陣%子矩陣約束%反問題%最佳逼近
엄의반중심대칭구진%자구진약속%반문제%최가핍근
Generalized anti-centrosymmetric matrices%Submatrix constraint%Inverse problem%Optimal ap-proximation
讨论了广义特征值反问题在子矩阵束约束下的广义反中心对称解及其最佳逼近问题。应用矩阵对的商奇异值分解,导出了该问题有广义反中心对称解的充要条件及有解情况下的通解表达式,证明了最佳逼近问题解的存在性与唯一性,并得到了最佳逼近解的表达式。
討論瞭廣義特徵值反問題在子矩陣束約束下的廣義反中心對稱解及其最佳逼近問題。應用矩陣對的商奇異值分解,導齣瞭該問題有廣義反中心對稱解的充要條件及有解情況下的通解錶達式,證明瞭最佳逼近問題解的存在性與唯一性,併得到瞭最佳逼近解的錶達式。
토론료엄의특정치반문제재자구진속약속하적엄의반중심대칭해급기최가핍근문제。응용구진대적상기이치분해,도출료해문제유엄의반중심대칭해적충요조건급유해정황하적통해표체식,증명료최가핍근문제해적존재성여유일성,병득도료최가핍근해적표체식。
This paper deals with the generalized anti-centrosymmetric solution of a generalized inverse eigen-value problem with a submatrix pencil constraint. By using the quotient singular value decomposition( QSVD) of matrix pencil,the sufficient and necessary conditions for the problem having a generalized centrosymmetric solution are obtained,and the general solution is presented. The best approximation for a given matrix pencil under a given spectral constraint and a submatrix pencil constraint is also considered. The existence and the u-niqueness of the optimal approximation are proved,and the expression of the best approximation are derived. A numerical algorithm for solving the problems is prensented.