P-亚对称矩阵的反问题及其最佳逼近

P-亚对称矩阵的反问题及其最佳逼近

摘要

矩阵反问题在计算物理，系统设计，航空工程，振动设计等领域有着广泛的应用，因此，这个问题在国内外引起了广的兴趣，日益被人们所重视。本文研究了矩阵反问题AX=B有P-亚对称解的充要条件及解的表达式,并求出了最佳逼近解.

关键词: P---亚对称矩阵 矩阵反问题 奇异值分解 最佳逼近

P-subsymmetric matrix invers problem and its optimal approximation

ABSTRACT

The matrix inverse problem are widely used in the computation physics, the system design, the aeronautical engineering, domain and vibration design,and so authors all over the world of great interest to these problems.In this article,the sufficient and necessary conditions for matrix inverse problem AX=B has P-subsymmetric solution are obtained,and the general representation of such matrix is presented.In addition,in the solution set of the inverse problem,the expression of the best approximation solution is also given.

Keywords: P-subsymmetric matrix, Matrix inverse problem, Singular value decomposition, Optimal approximation

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