线性流形上的广义中心对称矩阵反问题
INVERSE PROBLEMS OF GENERALIZED CENTROSYMMETRIC MATRICES ON THE LINEAR MANIFOLD
查看参考文献14篇
|
文摘
|
设R∈Cn×n是满足R=RH=R-1≠±In的广义反射矩阵.若A∈Cn×n满足RAR=A,则称A为n阶广义中心对称矩阵,n阶广义中心对称矩阵的全体记为GCSCn×n.令X1,Z1∈Cn×k1,Y1,W1∈Cn×l1,S={A|‖AX1-Z1‖2+‖Y1HA-W1H‖2=min,A∈GCSCn×n},本文研究如下问题.问题Ⅰ.给定矩阵Z2,X2∈Cn×k2,Y2,W2∈Cn×l2,求A∈S,使得f(A)=‖AX2-Z2‖2+‖Y2HA-W2H‖2=min,其中‖.‖是nobenius范数.问题Ⅱ.给定矩阵A∈Cn×n,求A∈SE,使得‖(~A)-(^A)‖=infA∈SL‖(~A)-A‖其中SE是问题Ⅰ的解集合.本文给出了问题Ⅰ解集合SE的表达式,并导出了矩阵方程AX2=Z2,Y2HA=W2H有解A∈S的充分必要条件及其通解表达式,并给出了问题Ⅱ解的表达式以及求解问题Ⅱ的数值方法和数值例子. |
|
其他语种文摘
|
Let R∈Cn×n satisfying R = RH=R-1≠±In be a nontrivial generalized reflexive matrix. A∈Cn×n is said to be generalized centrosymmetric if RAR = A. The set of all n×n generalized centrosymmetric matrices is denoted by GCSCn×n. Let X1,Z1∈Cn×k1,Y1,W1∈Cn×l1,S = {A|‖AX1-Z1‖2+‖Y1HA-W1H‖2= min, A∈GCSCn×n}. The following problems are considered. Problem Ⅰ. Given Z2,X2∈ Cn×k2;Y2,W2 ∈Cn×l2, find A∈S such that where ‖·‖ is the Frobenius norm. Problem Ⅱ. Given A∈Cn×n, find A ∈ SE such that where SE is the solution set of Problem I.The general form of the solution set SE of Problem I is given.Sufficient and necessary conditions for matrix equations AX_2=Z_2, Y~H_2A=W~H_2 having a solution A∈S are derivced, and the general solutions are given. The expression of the solution to Problem II is presented.A numbercal emple is provided. |
|
来源
|
计算数学
,2005,27(4):383-394 【核心库】
|
|
关键词
|
广义中心对称矩阵
;
反问题
;
线性流形
;
最佳逼近
|
|
地址
|
南京航空航天大学理学院, 江苏, 南京, 210016
|
|
语种
|
中文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
0254-7791 |
|
学科
|
数学 |
|
基金
|
国家自然科学基金项目
|
|
文献收藏号
|
CSCD:2129850
|
参考文献 共
14
共1页
|
|
1.
H C Chen. special properties and applications[J].
SIAM J.Matrix Anal. Appl.,1998,19:140-153
|
CSCD被引
23
次
|
|
|
|
|
2.
W F Trench. Linear Algebra Appl.
Linear Algebra Appl.,2004,377:207-218
|
CSCD被引
14
次
|
|
|
|
|
3.
W F Trench. Inverse eigenproblems and associated approximation problems for matrices with generalized symmetry or skew symmetry[J].
Linear Algebra Appl,2004,380:199-211
|
CSCD被引
14
次
|
|
|
|
|
4.
A L Andrew. Eigenvectors of certain matrices[J].
Linear Algebra Appl,1973,7:151-162
|
CSCD被引
6
次
|
|
|
|
|
5.
A L Andrew. Solution of equations involving centrosymmetric matrices[J].
Technometrics,1973,15:405-407
|
CSCD被引
1
次
|
|
|
|
|
6.
A L Andrew. Centrosymmetric matrices[J].
SIAM Rev,1998,40:697-698
|
CSCD被引
9
次
|
|
|
|
|
7.
A Cantoni. Linear Algebra Appl.
Linear Algebra Appl,1976,13:275-288
|
CSCD被引
8
次
|
|
|
|
|
8.
I J Good. The inverse of a centrosymmetric matrix[J].
Technometrics,1970,12:925-928
|
CSCD被引
1
次
|
|
|
|
|
9.
W C Pye. The pseudoinverse of a centrosymmetric matrix[J].
Linear Algebra Appl,1973,6:201-204
|
CSCD被引
4
次
|
|
|
|
|
10.
J R Weaver. Centrosymmetric (cross-symmetric) matrices.
Amer Math Monthly,1985,92:711-717
|
CSCD被引
16
次
|
|
|
|
|
11.
F Z Zhou. The solvability conditions for the inverse eigenvalue problems of centro-symmetric matrices[J].
Linear Algebra Appl,2003,364:147-160
|
CSCD被引
12
次
|
|
|
|
|
12.
戴华. 线性流形上的逆特征值问题.
高等学校计算数学学报,1995,17:357-366
|
CSCD被引
2
次
|
|
|
|
|
13.
张磊. 一类逆特征值问题.
数学物理学报,1993,13:94-99
|
CSCD被引
22
次
|
|
|
|
|
14.
戴华.
矩阵论,2001
|
CSCD被引
76
次
|
|
|
|
|
了解气象卫星更多信息，请访问