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ON SOLUTIONS OF matrix EQUATION AXAT ＋ BYBT=C

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Journal of Computational Mathematics 2005年第1期23卷 17-26页

作者： Yuan-beiDeng Xi-yanHu ICMSEC AcademyofMathematicsandSystemSciencesChineseAcademyofSciencesBeijing100080China CollegeofMathematicsandEconometrics HunanUniversityChangsha310082China

By making use of the quotient singular value decomposition (QSVD) of a matrix pair,this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the general solutions of the linear matrix equation AXA^T+BYB^T=C with the unknown X and Y, which may be both symmetric, skew-symmetric, nonnegativede finite, positive definite or some cross combinations respectively. Also, the solutions of some optimal problems are derived.

关键词： matrix equation matrix norm QSVD constrained condition optimal problem

Least-Squares Solution of Inverse Problem for Hermitian Anti-reflexive Matrices and Its Appoximation

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Acta Mathematica Sinica,English Series 2006年第2期22卷 477-484页

作者： Zhen Yun PENG Yuan Bei DENG Jin Wang LIU Department of Mathematics Hunan University of Science and Technology Department of Mathematics Central South University Institute of Computational Mathematics Chinese Academy of Sciences

In this paper, we first consider the least-squares solution of the matrix inverse problem as follows： Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X, B we have minA ｜｜AX - B｜｜. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by SE. Then the matrix nearness problem for the matrix inverse problem is discussed. That is： Given an arbitrary A^＊, find a matrix A E SE which is nearest to A^＊ in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.

关键词： hermitian reflexive matrix hermitian anti-reflexive matrix matrix norm nearest matrix

ON L^p-MATRICIALLY normED SPACES

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Acta Mathematica Scientia 2005年第4期25卷 681-686页

作者： T.别克 College of Mathematics and Systems Science Xinjiang University Urumqi 830046 China

It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially norm... 详细信息

关键词： matrix norm Lp-matricially normed space completely bounded operator

EQUISTABILITY OF THE matrix DIFFERENTIAL EQUATIONS

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Annals of Differential Equations 1998年第2期14卷 215-221页

作者：王林山聊城师范学院

In this paper the problem about equistability of the matrix equistability of the matrix differential equations have been discussed, and some criteria for equistability have been given.

关键词： matrix differential equations matrix norm matrix Lyapunov function equistability.

STABILITY ANALYSIS FOR LINEAR DELAY DIFFERENTIAL EQUATIONS AND NUMERICAL EXAMPLES

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Applied Mathematics(A Journal of Chinese Universities) 2003年第4期18卷 390-402页

作者： Sun Leping College of Mathematical Sciences,Shanghai normal University,Shanghai 200234,China. College of Mathematical Sciences Shanghai Normal University Shanghai China

The asymptotic stability of delay differential equation x′(t)=Ax(t)+Bx(t τ) is concerned with,where A,B∈C d×d are constant complex matrices, x(t τ)=(x 1(t-τ 1),x 2(t-τ 2),...,x d(t-τ d))T,τ k>0(k=1,...,d) stand for constant delays. Two criteria through evaluation of a harmonic function on the boundary of a certain region are obtained. The similar results for neutral delay differential equation x′(t)=Lx(t)+Mx(t-τ)+Nx′(t-τ) are also obtained,where L,M and N∈C d×d are constant complex matrices and τ>0 stands for constant delay. Numerical examples are showed to check the results which are more general than those already reported.

关键词： eigenvalue matrix norm spectral radius boundary criteria asymptotic stability harmonic function logarithmic norm

线性流形上一类对称广义中心对称矩阵的最佳逼近问题

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高等学校计算数学学报 2010年第1期32卷 29-36页

作者：谢冬秀刘仲云北京信息科技大学数学系长沙理工大学数学与计算科学学院

1问题的提出为叙述方便起见,首先介绍本文中出现的符号.设SR;和OR;分别表示所有n阶实对称矩阵和正交矩阵的集合,A;和‖A‖;分别表示A的Moore-Penrose广义逆和

关键词： symmetric generalized centro-symmetric matrix matrix norm linear manifold the optimal approximation

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双反对称矩阵反问题的最小二乘解

高等学校计算数学学报 2002年第3期24卷 199-205页

作者：盛炎平谢冬秀北京机械工业学院基础部北京机械工业学院基础部北京 100085

1 引言Rn×m表示所有n×m阶实矩阵集合,Rrn×m表示Rn×m中秩为r的子集;ORn×m表示所有n阶正交阵的集合;A+表示A的Moore-Penrose广义逆;Iκ表示κ阶单位阵;||·||表示Frobenius范数;ASRn×m表示n阶实反对称阵的全体;A＊B表示A与B的Hadam... 详细信息

1 引言Rn×m表示所有n×m阶实矩阵集合,Rrn×m表示Rn×m中秩为r的子集;ORn×m表示所有n阶正交阵的集合;A+表示A的Moore-Penrose广义逆;Iκ表示κ阶单位阵;||·||表示Frobenius范数;ASRn×m表示n阶实反对称阵的全体;A＊B表示A与B的Hadamard乘

关键词： anti-bisymmetric matrices matrix norm optimal approximation.

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对称自正交相似矩阵的逆特征值问题

高等学校计算数学学报 2004年第4期26卷 351-357页

作者：盛炎平王来生中国农业大学理学院中国农业大学理学院北京 100083 北京机械工业学院基础部北京 100085

1引言对称自正交相似矩阵在结构力学及土木工程等中有实际应用,在许多实际问题中会遇到其逆特征值问题.因此研究此问题是有意义的.

关键词： Symmetric and self-orthogonal similar matrix matrix norm optimal approximation.

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对称次反对称矩阵的一类反问题

高等学校计算数学学报 2003年第2期25卷 144-152页

作者：彭振贇胡锡炎张磊湖南大学应用数学系娄底 4170000 长沙410082 湖南大学应用数学系长沙 410082/娄底师专数学系

1 引言用R,SR,ASR,OR分别表示所有m×n实矩阵,n阶实对称矩阵,n阶实反对称矩阵和n阶实正交矩阵组成的集合,I表示k阶单位矩阵,S表示k阶反序单位矩阵,||A||表示矩阵A的Frobenius范数。若A=(a)∈R,记D=diag(a,a,…,a),L=(l)∈R其中当i>j时,... 详细信息

1 引言用R,SR,ASR,OR分别表示所有m×n实矩阵,n阶实对称矩阵,n阶实反对称矩阵和n阶实正交矩阵组成的集合,I表示k阶单位矩阵,S表示k阶反序单位矩阵,||A||表示矩阵A的Frobenius范数。若A=(a)∈R,记D=diag(a,a,…,a),L=(l)∈R其中当i>j时,l=a,当i≤j时,l=0,(i,j=1,2,…,n).若A=(a),B=(b)∈R,A*B表示A与B的Hadamard乘积,其定义为A*B=(ab)。

关键词： matrix norm symmetric and skew anti-symmetric matrix inverse problem the optimal approximation.