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LEAST—SQUARES SOLUTIONS OF X^TAX=B OVER POSITIVE SEMIDEFINITE MATRIXES A
作者姓名:Dongxiu  Xie
作者单位:Dongxiu Xie+ (Beijing Insititute of Machinery Industry,Beijing,10085,P.R,China) Lei Zhang (Hunan Computing Center,Changsha,410012,P.R. China)
基金项目:Supported by the National Nature Science Fundation of China.
摘    要:This paper is mainly concerned with solving the following two problems: Problem Ⅰ. Given X ∈ Rn×m, B . Rm×m. Find A ∈ Pn such thatwhereProblem Ⅱ. Given A ∈Rn×n. Find A ∈ SE such thatwhere F is Frobenius norm, and SE denotes the solution set of Problem I.The general solution of Problem I has been given. It is proved that there exists a unique solution for Problem II. The expression of this solution for corresponding Problem II for some special case will be derived.

关 键 词:最小平方解  正半定矩阵  Frobenins范数  凸锥  Hilbert空间  矩阵方程

LEAST-SQUARES SOLUTIONS OF X~TAX = B OVER POSITIVE SEMIDEFINITE MATRIXES A
Dongxiu Xie.LEAST-SQUARES SOLUTIONS OF X~TAX = B OVER POSITIVE SEMIDEFINITE MATRIXES A[J].Journal of Computational Mathematics,2003,21(2):167-174.
Authors:Dongxiu Xie
Abstract:
Keywords:positive semidefinite matrix  Least-square problem  Probenins norm  
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