| THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE |
| |
| 作者姓名： | Zhen-yun Peng |
| |
| 作者单位： | Zhen-yun Peng
(College of Mathematics and Econometrics，Hunan University，Changsha 410082，China) (Department of Mathematics，Loudi Teachers College，Loudi 417000，China)
Xi-yan Hu Lei Zhang (College of Mathematics and Econometrics，Hunan University，Changsha 410082，China) |
| |
| 基金项目： | Research supported by National Natural Science Foundation of China(10171031)，by Hunan Province Education Foundation(02C025) |
| |
| 摘 要： | In this paper, the following two problems are considered:Problem Ⅰ. Given S∈E Rn×p,X,B 6 Rn×m, find A ∈ SRs,n such that AX = B, where SR8,n = {A∈ Rn×n|xT(A - AT) = 0, for all x ∈ R(S)}.Problem Ⅱ. Given A* ∈ Rn×n, find A ∈ SE such that ||A-A*|| = minA∈sE||A-A*||, where SE is the solution set of Problem Ⅰ.The necessary and sufficient conditions for the solvability of and the general form of the solutions of problem Ⅰ are given. For problem Ⅱ, the expression for the solution, a numerical algorithm and a numerical example are provided.
|
| 关 键 词： | 逆问题 局部对称矩阵 可解性 Moore-Penrose广义逆 Frobenius范数 奇异值分解 |
THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE |
| |
| Zhen-yun Peng.THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE[J].Journal of Computational Mathematics,2003,21(4):505-512. |
| |
| Authors: | Zhen-yun Peng |
| |
| Abstract: | |
| |
| Keywords: | Part symmetric matrix Inverse problem Optimal approximation |
| 本文献已被 CNKI 等数据库收录！ |
