湖北民族学院学报：自然科学版
湖北民族學院學報：自然科學版
호북민족학원학보：자연과학판
Journal of Hubei Institute for Nationalities(Natural Sciences)
2011年
3期
241-244
,共4页
对称广义中心对称矩阵%最小二乘解%最佳逼近
對稱廣義中心對稱矩陣%最小二乘解%最佳逼近
대칭엄의중심대칭구진%최소이승해%최가핍근
symmetric and generalized centro-symmetric matrices%least-square solution%optimal approximation
研究了对称广义中心对称矩阵反问题的最小二乘解,得到了解的一般表达式,并就该问题的特殊情形矩阵反问题,得到了有解的充分必要条件及解的通式.此外,证明了最佳逼近问题解的存在唯一性,并给出了其解的具体表达式.
研究瞭對稱廣義中心對稱矩陣反問題的最小二乘解,得到瞭解的一般錶達式,併就該問題的特殊情形矩陣反問題,得到瞭有解的充分必要條件及解的通式.此外,證明瞭最佳逼近問題解的存在唯一性,併給齣瞭其解的具體錶達式.
연구료대칭엄의중심대칭구진반문제적최소이승해,득도료해적일반표체식,병취해문제적특수정형구진반문제,득도료유해적충분필요조건급해적통식.차외,증명료최가핍근문제해적존재유일성,병급출료기해적구체표체식.
The least-square solutions of inverse problems for symmetric and generalized centro-symmetric matrices are discussed,and the general expressions are given.For the special case of the least-square problem the inverse problem of the matrices,the necessary and sufficient conditions for the solvability and the general solutions of the problem are obtained.Moreover,the uniqueness of optimal approximation solution is proved,and its concrete expression is given.
