| 主子矩阵约束下矩阵反问题XTAX=B的对称解及其最佳逼近 |
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| 引用本文： | 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 |
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| 作者姓名： | 郭丽杰 周硕 |
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| 作者单位： | 东北电力大学 理学院, 吉林 吉林 132012 |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | 子矩阵约束 反问题 对称解 商奇异值分解 最佳逼近, |
| 收稿时间： | 2012-04-01 |
Optimal Approximation and Symmetric Solutions of Matrix Inverse Problem X~TAX=Bunder a Submatrix Constraint |
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| GUO Li-jie,ZHOU Shuo. Optimal Approximation and Symmetric Solutions of Matrix Inverse Problem X~TAX=Bunder a Submatrix Constraint[J]. Journal of Jilin University: Sci Ed, 2012, 50(6): 1075-1080 |
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| Authors: | GUO Li-jie ZHOU Shuo |
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| Affiliation: | College of Science, Northeast Dianli University, Jilin 132012, Jilin Province, China |
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| 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=Bunder a submatrix constraint. Moreover, the optimal approximation problem to a given matrix in the solution set wasconsidered, and the optimal approximation symmetric solution was obtained. |
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| Keywords: | submatrix constraint inverse problem symmetric solutions quotient singular value decomposition(QSVD) optimal approximation |
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