主子阵约束下广义自反矩阵的广义特征值反问题  

Inverse Generalized Eigenvalue Problem for Generalized Reflexive Matrices under a Submatrix Constraint

作　　者：周硕[1] 韩明花[1] 季本明 

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《吉林大学学报（理学版）》2013年第6期1029-1036,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11072085);吉林省自然科学基金(批准号:201115180)

摘　　要：利用矩阵的奇异值分解和商奇异值分解,建立子矩阵约束下广义特征值反问题的广义自反解存在的充分必要条件,并给出通解的表达式.对任意给定矩阵的最佳逼近问题,得到了最佳逼近广义自反解,并对最佳逼近解进行扰动分析.Using the singular value decomposition （SVD） and quotient singular value decomposition （QSVD） of a matrix and matrix pair,the authors established the necessary and sufficient conditions for the existence of the generalized reflexive solutions and the expressions for the inverse generalized eigenvalue problem of a matrix under a submatrix constraint,Moreover,the optimal approximation problem to a given matrix in the solution set was considered,and the optimal approximation generalized reflexive solution was obtained,and the perturbation analysis was made.

关 键 词：子矩阵约束 广义特征值反问题 广义自反解 最佳逼近 扰动分析 

分 类 号：O151.21[理学—数学]