CAJ | 학술논문

本文讨论广义特征值反问题在子矩阵束约束下的中心对称解及其最佳逼近问题.应用矩阵束的广义奇异值分解,导出了该问题有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.最后给出了求解最佳逼近问题的数值算法及数值例子.
본문토론엄의특정치반문제재자구진속약속하적중심대칭해급기최가핍근문제.응용구진속적엄의기이치분해,도출료해문제유중심대칭해적충요조건급유해정황하적통해표체식,증명료최가핍근문제해적존재성여유일성,병득도료최가핍근해적표체식.최후급출료구해최가핍근문제적수치산법급수치례자.
@@@@This paper deals with the centrosymmetric solution of a generalized inverse eigen-value problem with a submatrix pencil constraint. By using the generalized singular value decomposition(GSVD) of matrix pencils, the su?cient and necessary conditions for the prob-lem having a 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 uniqueness of the optimal approx-imation are proved, and the expression of the best approximation are derived. A numerical algorithm for solving the problems is prensented.