主子矩阵约束下矩阵反问题X^TAX=B的对称解及其最佳逼近  

Optimal Approximation and Symmetric Solutions of Matrix Inverse Problem X^TAX=Bunder a Submatrix Constraint

作　　者：郭丽杰[1] 周硕[1] 

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）》2012年第6期1075-1080,共6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,建立子矩阵约束下的矩阵反问题XTAX=B对称解存在的充分必要条件,并给出了通解的表达式,得到了最佳逼近对称解.Based on the singular value decomposition （SVD） and quotient singular value decomposition （QSVD） of a matrix and matrix pair, the necessary and sufficient conditions were established for the existence of the symmetric solutions and the expressions for the inverse problem of a matrix XTAX= B under a submatrix constraint. Moreover, the optimal approximation problem to a given matrix in the solution set was considered, and the optimal approximation symmetric solution was obtained.

关 键 词：子矩阵约束 反问题 对称解 商奇异值分解 最佳逼近 

分 类 号：O151.21[理学—数学]