中心主子阵约束下广义反中心对称矩阵的二次特征值反问题  

Inverse Quadratic Eigenvalue Problem for Generalized Anti-Centrosymmetric Matrices Under A Centro Submatrix Constraint

作　　者：郭丽杰[1] 韩明花[1] 周硕[1] Guo Lijie;Han Minghua;Zhou Shuo(Science College,Northeast Electric Power University,Jilin Jilin 132012)

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《东北电力大学学报》2018年第3期84-89,共6页Journal of Northeast Electric Power University

摘　　要：利用矩阵的奇异值分解和商奇异值分解,建立了中心主子阵约束下二次特征值反问题的广义反中心对称解存在的充分必要条件,并给出了通解的表达式.进而,考虑了对任意给定矩阵的最佳逼近问题,得到了最佳逼近广义反中心对称解.Using the singular value decomposition（ SVD） and quotient singular value decomposition（ QSVD）of a matrix and matrix pair,this paper establishes the necessary and sufficient conditions for the existence of the generalized Anti-centrosymmetric solutions and the expressions for the Inverse quadratic eigenvalue problem of a matrix under a centro submatrix constraint.Moreover,the optimal approximation problem to a given matrix in the solution set is considered,and the optimal approximation generalized Anti-centrosymmetric solution is obtained.

关 键 词：中心主子阵约束 二次特征值反问题 广义反中心对称解 商奇异值分解 最佳逼近 

分 类 号：O151.21[理学—数学]