【摘要】 本文首先研究矩阵方程约束下的两类最佳逼近问题,这两类问题是IELS问题、矩阵谱约束下最佳逼近问题和加权最小二乘问题等最佳逼近问题的一般形式。然后应用奇异值分解理论,根据最佳逼近的充要条件证明了第一类问题解的存在性及第二类问题解的唯一性,同时证明了这两类最佳逼近问题解的具体形式,最后给出了可用于计算机求解的解法步骤。更多还原

【Abstract】 This paper first research two problems of best approximation restricted by matrix,and this two problems are the generalization of the problem of IELS,best approximation restricted by matrix spectrum and weighted least squares estimate.Then the paper applies singular value decomposition(SVD)theory to prove the existence of the solution according to the necessary and sufficient conditions of the best approximation.At the end of this paper we provide a solution step that can be used in computer.更多还原