A = （aij） Rn×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSRn×n Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Pro...A = （aij） Rn×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSRn×n Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Problem Ⅰ. Given X Rn×m, B Rn×m. Find A S such that Problem Ⅱ. Given A* E Rn×n. Find A SE such that Where is Frobenius norm, and SE is the solution set of Problem I. In this paper the general representation of SE has been given. The necessary and sufficient conditons have been presented for Problem I0. For Problem Ⅱ the expression of the solution has been provided.展开更多
In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold, the necessary and sufficient conditions for the solvability of the inverse problem and the expression of the genera...In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold, the necessary and sufficient conditions for the solvability of the inverse problem and the expression of the general solution are given; at the same time, the best approximation problem is considered, the expression of the best approximate solution and the numerical method are also given. This paper extends the results in [1, 2].展开更多
The two classes of best approximation of a matrix on the linear manifold are discussed by using the row string operator and the generalized singular value decomposition of a matrix. The solutions of the problems and a...The two classes of best approximation of a matrix on the linear manifold are discussed by using the row string operator and the generalized singular value decomposition of a matrix. The solutions of the problems and a numerical method for solving the problems are given. The problems discussed in some papers could be subsumed in the cases proposed in this paper.展开更多
This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution ar...This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.展开更多
文摘A = （aij） Rn×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSRn×n Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Problem Ⅰ. Given X Rn×m, B Rn×m. Find A S such that Problem Ⅱ. Given A* E Rn×n. Find A SE such that Where is Frobenius norm, and SE is the solution set of Problem I. In this paper the general representation of SE has been given. The necessary and sufficient conditons have been presented for Problem I0. For Problem Ⅱ the expression of the solution has been provided.
文摘In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold, the necessary and sufficient conditions for the solvability of the inverse problem and the expression of the general solution are given; at the same time, the best approximation problem is considered, the expression of the best approximate solution and the numerical method are also given. This paper extends the results in [1, 2].
基金This works is supported by the National Natural Science Foundation of China(No.10261004).The first author was supported by Visiting Scholar Foundation of Key Lab.in University and Natural Science Foundation of Inner Mongolia(20010901-06)
文摘The two classes of best approximation of a matrix on the linear manifold are discussed by using the row string operator and the generalized singular value decomposition of a matrix. The solutions of the problems and a numerical method for solving the problems are given. The problems discussed in some papers could be subsumed in the cases proposed in this paper.
基金This work was supposed by the National Nature Science Foundation of China
文摘This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.
