摘要
This paper considers the following two problems:Problem I： Give X, B∈R^n×m, find A∈SAR^n×n such that AX = B Where SAR^n×n is the set of all n×n symmetric and sub-anti-symmetric matrices. Problem Ⅱ: Give A^～∈R^n×n find A^∈ SE such that ‖A^～-A^‖= minA∈SE‖A^～-A‖ Where SE is the solution set of problem I, ‖·‖ is the Frobenius norm. The necessary and sufficient conditions are studied for the set SE to be nonempty set, the general form of SE is given. For problem II, the expression of the solutionis provided.
This paper considers the following two problems:
Problem Ⅰ : Give X, Be Rn×m, find A ∈SARn×n such that
AX = B
Where SARn×n is the set of all nxn symmetric and sub-anti-symmetric matrices. Problem Ⅰ: Give A ∈ Rn×n find A ∈ SE such that
Where SE is the solution set of problem Ⅰ , ||·|| is the Frobenius norm.
The necessary and sufficient conditions are studied for the set SEto be nonempty set, the general form of SEis given. For problem Ⅱ the expression of the solution is provided.
出处
《计算数学》
CSCD
北大核心
2004年第1期73-80,共8页
Mathematica Numerica Sinica
基金
国家自然科学基金资助项目(10171031)
北京市优秀人才专项经费资助项目(020320).
关键词
对称次反对称矩阵
反问题
范数
特征值
最小二乘解
Symmetric and sub-anti-symmetric matrics, matrix norm, optimal approximation
