ON OPTIMAL APPROXIMATION OF A MATRIX UNDER SPECTRAL RESTRICTION
谱约束下的矩阵最佳逼近问题

The problem of optimal approximation of a matrix under given spectral restrictionis proposed in the processes of test or recovery of linear systems. A preliminary esti-mate A of the unknown matrix A can be obtained by the experimental observation va-lues and the information of statistical distribution. The optimal estimate of A is sucha matrix A that satisfies the given spectral restriction for A and is the best approxima-tion of A. In this paper we study the existence and uniquencess of A Furthermore,a practical procedure is provided by means of generalized inverse and best approxima-tion for the purpose of computation.