双反对称矩阵反问题的最小二乘解  

LEAST-SQUARE SOLUTIONS OF INVERSE PROBLEMS FOR ANTI-BISYMMETRIC MATRICES

作　　者：盛炎平[1] 谢冬秀[1] 

机构地区：[1]北京机械工业学院基础部,北京100085

出　　处：《高等学校计算数学学报》2002年第3期199-205,共7页Numerical Mathematics A Journal of Chinese Universities

摘　　要：A = (aij) ∈ Rn×n is called anti-bisymmetric matrix if aij＝-aij,aij =-an-j+1,,n-i+1,i ,j＝1,2,… ,n. We denoted the set of all n × n anti-bisymmetric ma-trices by ABSRin×n. In this paper, we discuss the following two problems:Problem I: Given X,B∈Rn×n, find A∈ABSRn×n such that ‖ AX-B ‖＝mix, where ‖‖ is the Frobenius norm.Problem I: Given X,B∈Rn×n, find A∈ABSRn×n such that ‖ A* -A ‖ =inf ‖ A* -A‖ , where SE is the solution set of Problem I .A∈SEFor problem I , the general form of SE has been given. For problem I , theexpression of the solution has been provided.A=(aij)∈Rn×n is called anti-bisymmetric matrix if aij=-aji,aij=-an-j+1,n-i+1,i,j=1,2,… ,n. We denoted the set of all n*n anti-bisymmetric matrices by ABSRn×n. In this paper, we discuss the following two problems:Problem Ⅰ , Given X,B∈Rn×m, find A∈ABSRn×m such that ||AX-B|| = mix, where || || is the Frobenius norm.Problem Ⅱ : Given X,B∈Rn×m, find A∈ABSRn×n such that || A∈-A || =inf || A∈ -A || , where SE is the solution set of Problem Ⅰ . A∈SEFor problem Ⅰ , the general form of SE has been given. For problem Ⅱ , the expression of the solution has been provided.

关 键 词：双反对称矩阵 反问题 最小二乘解 

分 类 号：O241.6[理学—计算数学]