Least Square Speical Type Solution Of A Series Of Linear Matrix Equation With The Least Norm

The problem of solving the linear matrix equation is one of the important research fields of the numerical linear algebra, it has many applications in biology, electricity chanics, parameter, identification, automatic control theory, linear optimal control and so on, because of this, Makes the problem of solving the matrix equation for calculating the field of mathematics one of the most popular research topics。This article focuses on the following two questions:Problem I Given Ai∈Rm×s, Bi∈Rsi×n,C∈Rm×n, find Xi∈H(?)Rsi×si, i=1,2,...,t, such thatWhere H is solution set of constraints.Problem II Let HL denote the solution set of Problem Ⅰ,find Xi∈Rsi×si,i=1,2,..., t, such that:In this thesis, we mainly study Problem Ⅰ,Ⅱ when H is symmetric, antisymmetric matrix, diagonal, dual diagonal matrix, tridiagonal matrix, symmetric matrix。The main results are as follows:1. For questions I, we apply the Kronecker product and matrix Moore-Penrose generalized inverse,∑AiXiBi=C into Ax=b, and given the problem I on symmetric matrices, symmetric matrices, diagonal, dual diagonal matrix, tridiagonal matrix, dual symmetric matrix solution.2. For questions Ⅱ, we apply the Kronecker product and matrix Moore-Penrose generalized inverse,∑AiXiBi=C into Ax=b, and given the problem Ⅱ on symmetric matrices, symmetric matrices, diagonal, dual diagonal matrix, tridiagonal matrix, dual symmetric matrix solution,and Issues and problems are given Ⅰ Ⅱ numerical examples.