CAJ | 학술논문

文章首先考虑了如下问题：给定矩阵A，B∈Cn×m，求循环矩阵X∈CIRn×n，使得min｜｜AX—B｜｜。给X出了问题具有循环矩阵解的条件和解的一般表达式，若用SE表示上述问题解的集合，文章还考虑了最佳逼近问题：给定X＊∈CIRn×n，求X∈SE，使得minX∈SE｜｜X-X＊｜｜=｜｜X-X＊｜｜，其中｜｜·｜｜表示矩阵的Frobenius范XESE数，证明了问题存在唯一解，给出了其唯一解的一般表达式。
문장수선고필료여하문제：급정구진A，B∈Cn×m，구순배구진X∈CIRn×n，사득min｜｜AX—B｜｜。급X출료문제구유순배구진해적조건화해적일반표체식，약용SE표시상술문제해적집합，문장환고필료최가핍근문제：급정X＊∈CIRn×n，구X∈SE，사득minX∈SE｜｜X-X＊｜｜=｜｜X-X＊｜｜，기중｜｜·｜｜표시구진적Frobenius범XESE수，증명료문제존재유일해，급출료기유일해적일반표체식。
In this paper, we first coneider the problelm as follow：Find a circulant matrix X∈CIRn×n such that for given matrics A,X∈Cn×m we have min ｜｜ AX - B ｜｜The existence theorems are obtained,and a general representation of such a matrix is presented. We denote the set of such ma- trices by SE. Then the matrix approximation problem is discussed. That is： Find a matrixX∈ SE such that for a given X∈ CIRn×n X∈CIRn×nwe have minX∈SE｜｜X-X＊｜｜=｜｜X-X＊｜｜ Where ｜｜·｜｜ is the Frobenius norm of matrics. We show that the approximation matrix is unique and provide an expression for thisapproximation matrix.