中心主子矩阵约束下矩阵反问题\bmX\bmA\bmX=\bmB的双对称解及其最佳逼近

周硕,王霖

系统科学与数学 ›› 2014, Vol. 34 ›› Issue (8) : 985-991.

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PDF(286 KB)
系统科学与数学 ›› 2014, Vol. 34 ›› Issue (8) : 985-991. DOI: 10.12341/jssms12393
论文

中心主子矩阵约束下矩阵反问题\bmX\bmA\bmX=\bmB的双对称解及其最佳逼近

    周硕,王霖
作者信息 +

INVERSE PROBLEM \bmX\bmA\bmX=\bmB OF BISYMMETRIC MATRICES SOLUTIONS WITH A CENTER PRINCIPAL SUBMATRIX CONSTRAINT AND ITS OPTIMAL APPROXIMATION

    ZHOU Shuo ,WANG Lin
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摘要

文章研究了中心主子矩阵约束下矩阵方程XTAX=B的双对称解.利用子空间的基将约束问题转化为非约束问题的方法,得到了有解的充分必要条件及解的一般表达式.进而,考虑了与之相关的任意给定矩阵的最佳逼近问题.

Abstract

This paper considers the bisymmetric matrices solutions of matrix equations XTAX=B for A under a central principal submatrix constraint. By the basis {\rm vec}tors of subspace, the constraint problem is transformed into a unconstraint problem, and necessary and sufficient conditions for the solvability and the general expression of the solutions are obtained. Moreover, we also obtain the expression of the solution to the related optimal approximation problem.

关键词

矩阵反问题 / 中心主子矩阵约束 / 双对称矩阵 / 最佳逼近.

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周硕 , 王霖. 中心主子矩阵约束下矩阵反问题\bmXT\bmA\bmX=\bmB的双对称解及其最佳逼近. 系统科学与数学, 2014, 34(8): 985-991. https://doi.org/10.12341/jssms12393
ZHOU Shuo , WANG Lin. INVERSE PROBLEM \bmXT\bmA\bmX=\bmB OF BISYMMETRIC MATRICES SOLUTIONS WITH A CENTER PRINCIPAL SUBMATRIX CONSTRAINT AND ITS OPTIMAL APPROXIMATION. Journal of Systems Science and Mathematical Sciences, 2014, 34(8): 985-991 https://doi.org/10.12341/jssms12393
中图分类号: 15A24    15A29   
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