矩阵多项式逆L-值问题的最佳逼近

ON BEST APPROXIMATION OF A PROBLEM ABOUT INVERSE LATENT VALUE OF MATRIX POLYNOMIALS

本文讨论了矩阵多项式的L-值逆问题的最佳逼近。如果已知m阶矩阵多项式的部分矩阵A_(j1),…,A_(jL),并且给定矩阵多项式的部分L—值和L—向量,本文证明了矩阵多项式中另一部分未知矩阵A_i,…,A_(ik)存在的充分必要条件。若以S表示未知矩阵A_i,…,A_(ik)解的全体,对于任意给定的矩阵A_(i1),…,A_(ik),本文还证明了A_(i1),…,A_(ik)在S中的最佳逼近A_(i1),…,Ai_k的存在唯一性并给出了计算最佳逼近A_(i1),…,A_(ik)具体算法。

This paper discusses the best approximation of the problem about inverselatent value of matrix polynomials. If we know some matrixes A_J_1,…, A_J_Lof a m-order matrix polynomial, and some latent values and latent vectorsof the matrix polynomial are given, this paper has proved the necessary andsufficient conditons for the existence to the other unkown matrixes A_i_1,…, A_i_k of the matrix polynomial. If S represents all the solutions of A_i_1,…, A_i_k, for any matrixesA_i_1, …, A_i_k, it will prove the existence and unqu-eness of the solution which is the best approximation(A_i_1,…, A_i_k)to (A_i_1,…, A_i_k) in S. A pratical proledure for computing (A_i_1, …, A_i_k) is given.