吉林大学学报（理学版）2012，Vol.50Issue(6)：1075-1080,6.
主子矩阵约束下矩阵反问题XTAX=B的对称解及其最佳逼近
Optimal Approximation and Symmetric Solutions of Matrix Inverse Problem XTAX=B under a Submatrix Constraint
摘要
Abstract
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Key words
submatrix constraint/ inverse problem/ symmetric solutions/ quotient singular value decomposition(QSVD)/ optimal approximation分类
数理科学引用本文复制引用
郭丽杰,周硕..主子矩阵约束下矩阵反问题XTAX=B的对称解及其最佳逼近[J].吉林大学学报（理学版）,2012,50(6):1075-1080,6.基金项目
国家自然科学基金(批准号:11072085)和吉林省自然科学基金(批准号:201115180). （批准号:11072085）
