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
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文摘
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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. |
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其他语种文摘
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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. |
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来源
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计算数学
,2005,27(4):383-394 【核心库】
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关键词
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广义中心对称矩阵
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反问题
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线性流形
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最佳逼近
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地址
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南京航空航天大学理学院, 江苏, 南京, 210016
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-7791 |
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学科
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数学 |
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基金
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国家自然科学基金项目
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文献收藏号
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CSCD:2129850
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