一类反对称次对称矩阵反问题的最小二乘解  

THE LEAST-SQUARES SOLUTION OF INVERSE PROBLERM OVER ANTI-SYMMETRIC AND PERSYMMETRIC MATRICES

作　　者：谢冬秀[1] 廖安平[2] 

机构地区：[1]北京机械工业学院,北京100085 [2]湖南大学应用数学系

出　　处：《数值计算与计算机应用》2003年第4期304-313,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金;北京优秀人才专项经费资助

摘　　要：§1.问题的提出 Rn×m表示所有n×m阶实对称阵集合,Rn=Rn×1,Rn×m r表示Rn×m中秩为r的子集,On是n阶正交阵之集,Sn表示n阶实对称阵的全体,A+表示A的Moorepenrose广义逆,Ik表示k阶单位阵,Sk=(ek,ek-1,…,e1)∈Rk×k,其中ei为单位阵Ik的第i列.In this paper, we are concerned with the following two problems: Problem 1 we describe the set ASnE of real n -by-n anti-symmetric and persymmetric matrices such that minimize the Frobenius norm of AX - B for X, B in Rnxn; Problem 2 find the unique A in the set ASnE, satisfying ||A*- A|| - min ||A* - A||, where A* ∈ Rnxn is a given matrix, || ·|| is the Frobenius norm. We derive a general expression of the set ASnE. For Problem 2, we prove the existence and the uniqueness of the solution and provide the expression of this unique solution. We also report some numerical results to support the theory established in the paper.

关 键 词：反对称次对称矩阵 最小二乘解 实对称矩阵 正交矩阵 HADAMARD乘积 

分 类 号：O241[理学—计算数学]