一类亚半正定矩阵的左右逆特征值问题

1．引言在工程技术中常常遇到这样一类逆特征值问题：要求在一个矩阵集合S中，找具有给定的部分右特征对（特征值及相应的特征向量）和给定的部分左特征对（特征值及相应的特征向量）的矩阵．文［2］，［3］讨论了S为。x。实矩阵集合的情形．文［4］－［7］对S为nxn实对称矩阵．对称正定矩阵，对称半正定矩阵集合的情形进行了讨论．文【川讨论了S为亚正定阵集合的情形．并提到了对于亚半正定矩阵的情形目下无人涉及，有待进一步研究．本文将对S为nxn亚半正定矩阵集合的情形进行讨论．给出了亚半正定矩阵的左右逆特征值问题有解的充要条件…     

流形上矩阵方程AX=B的正定及半正定阵的反问题

文[1-5]中研究了对称、对称半正定及流形上的对称半正定的反问题,并说明了其应用背景.本文研究线性流形上的正定及半正定阵的反问题,说明了文[1-3]中的一些结果为本文的特例.     

线性流形上亚半正定阵的一类逆特征值问题

1　引言与引理设 Rm× n表示所有 m× n实矩阵集合 ,m=n时 ,Rm× n简记为 Rm;Rm0 表示所有 m阶亚半正定阵集合 ,即 Rm0 ={ A∈Rm× m|YTAY≥ 0 , Y∈Rm× 1 } ;ORm表示 m阶正交矩阵集合 ;A+表示矩阵 A的 Moore-Penrose广义逆 ;‖·‖表示 Frobenius范数 .In 表示 n阶单位阵 ,有时令SE={ A∈ Rm× m|‖ AE -F‖ =min,E,F∈ Rm× k} ,(1 .1 )则 SE是线性流形 .文 [1 ] ,[2 ]分别研究了 SE上实对称矩阵及实对称半正定阵的逆特征值问题 ,本文将进一步研究 SE上亚半正定阵的一类逆特征值问题 ,具体叙述如下 :问题 　给定 X,B∈R…     

关于实对称半正定阵的几个结论

利用矩阵合同与交换的性质,运用矩阵运算技巧得到关于实对称半正定阵的若干性质,将实数的某些理论推广到实对称阵中.     

正定矩阵的子式阵仍是正定矩阵的一个充要条件

文[2]证明了实对称正定矩阵的子式阵仍然是实对称正定矩阵,文[3]给出了一般的正定矩阵的的概念,本文利用标准型给出了一般正定矩阵的子式阵仍然是正定矩阵的充要条件.     

复矩阵正定性的进一步拓广

实对称矩阵的正定性的研究已取得丰富的成果,并为众多学科所应用。随着应用问题的研究对实矩阵的正定性已有种种推广[1][2][4]。特别[2]对复正定 Hemite 阵作了推广。本文对复矩阵的正定性概念予以进一步拓广,建立了若干有趣的结果。     

正定矩阵的子式阵仍是正定矩阵的一个充要条件

文[2]证明了实对称正定矩阵的子式阵仍然是实对称正定矩阵,文[3]给出了一般的正定矩阵的的概念,本文利用标准型给出了一般正定矩阵的子式阵仍然是正定矩阵的充要条件．     

半正定矩阵及矩阵方程AX=B的反问题

文从研究一类控制系统的实际背景提出对已知实向量x,b求满足Ax=b的对称正定阵A的一类反问题。文[2]与[3]研究了上述反问题在对称正定类、正定类中有解的充要条件及解的一般形式。本文讨论复矩阵方程 AX=B(1)(X,B为m×n阵,A为m×m阵)在半正定、正定、H半正定、H正定类中反问题有解的充要条件及其解集的一般形式。如无特别申明,本文总考虑复矩阵和复向量,其共轭转置用“*”表     

亚正定阵理论(Ⅱ)

本文继续[Ⅰ]的讨论,建立了亚正定阵的行列式理论。给出了许多新的结果:例如广义Minkowski不等式、广义凸性不等式等等,对某些种类的亚正定阵,还将关于任意阵的行列式的Hadamard不等式作了改进。最后,将Open-heim关于正定阵的Hadamavd乘积的著名结果推广到亚正定阵上。     

亚正定阵的几个开问题及一些不等式

亚正定阵的几个开问题及一些不等式谢清明（湘潭大学数学系，湖南４１１１０５）关键词亚正定阵，ｋ－局部对称阵，Ｓｃｈｕｒ补．     

Bi-block positive semidefiniteness of bi-block symmetric tensors

The positive definiteness of elasticity tensors plays an important role in the elasticity theory.In this paper,we consider the bi-block symmetric tensors,which contain elasticity tensors as a subclass.First,we define the bi-block M-eigenvalue of a bi-block symmetric tensor,and show that a bi-block symmetric tensor is bi-block positive(semi)definite if and only if its smallest bi-block M-eigenvalue is(nonnegative)positive.Then,we discuss the distribution of bi-block M-eigenvalues,by which we get a sufficient condition for judging bi-block positive(semi)definiteness of the bi-block symmetric tensor involved.Particularly,we show that several classes of bi-block symmetric tensors are bi-block positive definite or bi-block positive semidefinite,including bi-block(strictly)diagonally dominant symmetric tensors and bi-block symmetric(B)B0-tensors.These give easily checkable sufficient conditions for judging bi-block positive(semi)definiteness of a bi-block symmetric tensor.As a byproduct,we also obtain two easily checkable sufficient conditions for the strong ellipticity of elasticity tensors.     

Three symmetric positive solutions for second-order nonlocal boundary value problems

Using the Leggett-Williams fixed point theorem,we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u(t)+g(t)f(t,u(t))=0,0相似文献   

On parallel multisplitting methods for symmetric positive semidefinite linear systems

In this paper we propose some parallel multisplitting methods for solving consistent symmetric positive semidefinite linear systems, based on modified diagonally compensated reduction. The semiconvergence of the parallel multisplitting method is discussed. The results here generalize some known results for the nonsingular linear systems to the singular systems. Copyright © 2008 John Wiley & Sons, Ltd.     

A class of modified block SSOR preconditioners for symmetric positive definite systems of linear equations

A class of modified block SSOR preconditioners is presented for solving symmetric positive definite systems of linear equations, which arise in the hierarchical basis finite element discretizations of the second order self‐adjoint elliptic boundary value problems. This class of methods is strongly related to two level methods, standard multigrid methods, and Jacobi‐like hierarchical basis methods. The optimal relaxation factors and optimal condition numbers are estimated in detail. Theoretical analyses show that these methods are very robust, and especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Multiple symmetric results for singular quasilinear elliptic systems with critical homogeneous nonlinearity

This paper deals with the existence and multiplicity of symmetric solutions for a class of singular quasilinear elliptic systems with critical homogeneous nonlinearity in a bounded symmetric domain. Applying variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G‐symmetric solutions under some appropriate assumptions on the weighted functions and the parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

Maximal- and minimal symmetric solutions of fully fuzzy linear systems

In this paper, we shall propose a new method to obtain symmetric solutions of a fully fuzzy linear system (FFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a FFLS (in the present paper, we assumed that the 1-cut of a FFLS is a crisp linear system or equivalently, the matrix coefficient and right hand side have triangular shapes), then some unknown symmetric spreads are allocated to each row of a 1-cut of a FFLS. So, after some manipulations, the original FFLS is transformed to solving 2n linear equations to find the symmetric spreads. However, our method always give us a fuzzy number vector solution. Moreover, using the proposed method leads to determining the maximal- and minimal symmetric solutions of the FFLS which are placed in a Tolerable Solution Set and a Controllable Solution Set, respectively. However, the obtained solutions could be interpreted as bounded symmetric solutions of the FFLS which are useful for a large number of multiplications existing between two fuzzy numbers. Finally, some numerical examples are given to illustrate the ability of the proposed method.     

Semiconvergence of parallel multisplitting methods for symmetric positive semidefinite linear systems

In this paper we construct some parallel relaxed multisplitting methods for solving consistent symmetric positive semidefinite linear systems, based on modified diagonally compensated reduction and incomplete factorizations. The semiconvergence of the parallel multisplitting method, relaxed multisplitting method and relaxed two‐stage multisplitting method are discussed. The results generalize some well‐known results for the nonsingular linear systems to the singular systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Existence and multiplicity of symmetric positive solutions for three-point boundary value problem

In this paper, we are concerned with the existence and multiplicity of symmetric positive solutions for the following second-order three-point boundary value problem

     

Asymptotically symmetric embeddings and symmetric quasicircles

A well-known characterization of quasicircles is the following: A Jordan curve in the complex plane is a quasicircle if and only if it is the image of the unit circle under a quasisymmetric embedding. In this paper we try to characterize a subclass of quasicircles, namely, symmetric quasicircles, by introducing the concept of asymptotically symmetric embeddings. We show that a Jordan curve in the complex plane is a symmetric quasicircle if and only if it is the image of the unit circle under an asymptotically symmetric embedding.

     

Landau-Lifshitz方程派生的球面锥对称族及其演化

直至2008年,尚未见到讨论同时具有外磁场和各向异性场的多维Landau-Lifshitz方程的显式动态解的文献.当缺少外加磁场或各向异性场时,许多作者曾经尝试过Hirota的著名方法,Lie代数结构与Backlund变换,双线性变换等,但精确解仍然没有构造出来.本文首先给出了一种求解具有外磁场和各向异性场的Landa...