一类分块矩阵的谱包含域

给出了一类复分块矩阵的谱包含域，推广与改进了文[1～5]的相应结果．     

关于Brualdi谱包含域的一点注记

关于矩阵的谱包含域的研究是矩阵分析领域中具有重要意义及广泛应用价值的课题．经典的结果有 Ｇｅｒｓｃｈｇｏｒｉｎ圆盘域, Ｃａｓｓｉｎｉ卵形域［１］． Ｂｒｕａｌｄｉ于 １９８２年按环路给出了新的诸包含域．这一阶段性成果改进了经典的圆盘域及卵形域［２,３］．但没有讨论到特征值的排除问题．本文在［２］的基础上给出了特征值的排除定理,改进了经典的Ｇｅｒｓｃｈｇｏｒｉｎ圆盘域及Ｃａｓｓｉｎｉ卵形域之排除定理． 在本文中,我们记全体ｎ阶复方阵的集合为Ｃ（Ａ）表Ａ＝（ａｉｊ）Ｃ的谱,即特征值集合．Ａ的方向图记作…     

矩阵复合型谱包含域的改进及应用

本文研究了矩阵的复合型谱包含域,给出了边界定理,得到了改进的复合型谱包含域,作为应用得到了非奇异H-矩阵的更精确的判别条件．     

Cassini卵形谱包含域的改进及应用

本文给出了改进的Cassini卵形谱包含域,讨论了相应的隔离定理及边界问 题,所得结果推广了文[1-4]的相应定理.作为应用得到了M-矩阵的一个新表征.     

关于复方阵数值域的包含域

本文首先讨论了最小包含域的等价表征，改进与推广了［１］－［３］的结果，其次利用降价法给出了一个新包含域     

关于可拓集合的运算

根据蔡文提出的可拓集合的新定义,给出了可拓集合的包含、并、交、非运算的新定义,并讨论了有关运算性质,进而获得可拓域与稳定域的几个交并运算结果.     

关于“块H-矩阵与块矩阵的谱”一文的注记

完善了"块H-矩阵与块矩阵的谱"一文中的主要结论.进一步,给出了分块矩阵特征值的一个新包含域,并用实例说明了新结论的优越性.     

凸域内矩形的运动测度

本文研究了凸域内矩形的运动测度,通过对凸域内定长线段运动测度的推广,建立了包含在凸域内且长、宽都确定的矩形运动测度的一般公式,利用此公式得到了圆域和矩形域内此类矩形的运动测度,并以此为基础得到了推广后的Buffon投针问题的一些结果.     

带Bergman度量的有界典型域上Laplace-Beltrami算子谱的下界

本文估计了带K?hler度量的有界典型域上Laplace-Beltrami算子谱的下界,给出了带K?hler度量的第二类有界典型域上Laplace-Beltrami算子谱的下界的范围.特别地,对于秩为1的区域,本文给出的结论与已有结论相一致.     

一类有界对称域上的Hartogs型域的自同构群

本文研究了稍微广泛的一类Hartogs型域的自同构群.利用华域的自同构群,获得了一类有界对称域上的Hartogs型域的自同构群的具体形式,推广了有界对称域上的Hartogs型域的自同构群这一结果.     

Spectral Inclusion Properties of Unbounded Hamiltonian Operators

In this paper, the authors investigate the spectral inclusion properties of the quadratic numerical range for unbounded Hamiltonian operators. Moreover, some examples are presented to illustrate the main results.     

求解大型稀疏最小二乘问题的2—块PSD型迭代法

１引言假设Ａ为大型稀疏的ｍ×ｎ实矩阵（ｍ＞ｎ）,ｒａｎｋ（Ａ）＝ｎ,在实际中,常常需要求解Ａｘ＝ｂ,（１．１）其中ｂ为给定的ｍ维向量．求（１．１）的欧氏范数最小二乘解等价于求解其中ｒ为ｍ维向量,不失一般性,可令其中Ａ;为ｎ×ｎ满秩方阵,且把ｂ和ｒ也相应地分块为其中ｒ１和ｂ１都是ｎ维向量,用（１．３）和（１．４）的符号,（１．２）可写成等价形式如下相应的块Ｊａｃｏｂｉ迭代矩阵Ｂ２和Ｂ３,定义为Ｃ相应于ＢＬ的分块形式是Ｌ循环阵或是ＧＣＯ（１,Ｌ—１）阵或Ｔ（１,ｌ—１）阵,ＢＬ是指标为Ｌ的弱循环阵（…     

Resolvent convergence and spectral approximations of sequences of self-adjoint subspaces

This paper studies resolvent convergence and spectral approximations of sequences of self-adjoint subspaces (relations) in complex Hilbert spaces. Concepts of strong resolvent convergence, norm resolvent convergence, spectral inclusion, and spectral exactness are introduced. Fundamental properties of resolvents of subspaces are studied. By applying these properties, several equivalent and sufficient conditions for convergence of sequences of self-adjoint subspaces in the strong and norm resolvent senses are given. It is shown that a sequence of self-adjoint subspaces is spectrally inclusive under the strong resolvent convergence and spectrally exact under the norm resolvent convergence. A sufficient condition is given for spectral exactness of a sequence of self-adjoint subspaces in an open interval lacking essential spectral points. In addition, criteria are established for spectral inclusion and spectral exactness of a sequence of self-adjoint subspaces that are defined on proper closed subspaces.     

Inclusion relations between certain sets of matrices

In this paper we study inclusion relations between the following four classes of matrices: normal matrices, matrices with equal spectral radius and spectral norm, matrices whose numerical range coincides with the convex polygon spanned by their eigenvalues, and matrices with equal numerical and spectral radii.     

Brauer-type bounds for Hadamard product of nonnegative tensors

In this paper, we establish some Brauer-type bounds for the spectral radius of Hadamard product of two nonnegative tensors based on Brauer-type inclusion set, which are shown to be sharper than the existing bounds established in the literature. The validity of the obtained results is theoretically and numerically tested.     

A new concept for block operator matrices:the quadratic numerical range

In this paper a new concept for 2×2-block operator matrices – the quadratic numerical range – is studied. The main results are a spectral inclusion theorem, an estimate of the resolvent in terms of the quadratic numerical range, factorization theorems for the Schur complements, and a theorem about angular operator representations of spectral invariant subspaces which implies e.g. the existence of solutions of the corresponding Riccati equations and a block diagonalization. All results are new in the operator as well as in the matrix case.