共查询到19条相似文献,搜索用时 46 毫秒
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矩阵对角占优性的推广及应用 总被引:37,自引:1,他引:37
§1.引言设 A=(a_(ij))_(n×n)为一复矩阵,若有一正向量 d=(d_1,d_2,…,d_n)~T 使得d_i|a_(ij)|≥sum from j≠1 d_j|a_(ij)|,(1)对每一 i∈N={1,2,…,n}都成立,则称 A 为广义对角占优矩阵,记为 A∈D_0~*;如若(1)式中每一不等号都是严格的,则称 A 为广义严格对角占优矩阵,记为 A∈D~*.特别地,当 d=(1,1,…,1)~T 时,A∈D_0~*及 A∈D~*即是通常的对角占优与严格对角占优,分别记作 A∈D_0及 A∈D.利用矩阵的对角占优性质讨论其特征值分布是矩阵论中的重要课题,文献[5]—[10]给出了这方面的重要结果.n 阶实方阵 A 称为 M-矩阵,如果 A具有形式:A=sI-B,s>ρ(B),其中 B 为 n 阶非负方阵,ρ(B)表 B 之谱半径,利用广义严格对角占优的概念,文[1]给出了 M-矩阵的等价表征:若 n 阶实方阵 相似文献
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给出了判定非广义对角占优矩阵的充要条件,从理论上彻底解决了不可约非广义对角占优矩阵的判定问题,并给出了判定不可约非广义对角占优矩阵的具体算法. 相似文献
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利用α-对角占优矩阵的性质,给出了判定广义对角占优矩阵的几个充分条件,改进了近期的一些结果,并用相应的数值实例说明了这些结果的有效性. 相似文献
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1 问题的提出一个n阶方阵Tn被称为Toeplitz矩阵,如果它满足 相似文献
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We obtain the exact values of some important approximative quantities (such as the best approximation, the basis width, Kolmogorov's width, and the best n-term approximation) of certain sets of images of the diagonal operators in the Orlicz sequence spaces l M . 相似文献
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Upper and lower bounds are established for the entropy numbersof certain diagonal operators between Banach sequence spaces.These diagonal operators are isomorphisms between the spacesconsidered in the paper and weighted sequence spaces consideredby Leopold so that the entropy numbers in question coincidewith those considered by Leopold. The results in the paper improvethe previous results in at least two ways. The estimates inthe paper are almost sharp in the sense that theupper and lower estimates differ only by logarithmic factorsfor a much wider range of parameters. Moreover, all the upperestimates are improvements on the previous ones, the improvementbeing quite significant in some cases. 相似文献
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Markus Weimar 《Journal of Fourier Analysis and Applications》2016,22(2):251-284
This paper is concerned with problems in the context of the theoretical foundation of adaptive algorithms for the numerical treatment of operator equations. It is well-known that the analysis of such schemes naturally leads to function spaces of Besov type. But, especially when dealing with equations on non-smooth manifolds, the definition of these spaces is not straightforward. Nevertheless, motivated by applications, recently Besov-type spaces \(B^\alpha _{\Psi ,q}(L_p(\Gamma ))\) on certain two-dimensional, patchwise smooth surfaces were defined and employed successfully. In the present paper, we extend this definition (based on wavelet expansions) to a quite general class of d-dimensional manifolds and investigate some analytical properties of the resulting quasi-Banach spaces. In particular, we prove that different prominent constructions of biorthogonal wavelet systems \(\Psi \) on domains or manifolds \(\Gamma \) which admit a decomposition into smooth patches actually generate the same Besov-type function spaces \(B^\alpha _{\Psi ,q}(L_p(\Gamma ))\), provided that their univariate ingredients possess a sufficiently large order of cancellation and regularity. For this purpose, a theory of almost diagonal matrices on related sequence spaces \(b^\alpha _{p,q}(\nabla )\) of Besov type is developed. 相似文献
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Yi Ming Zou 《代数通讯》2013,41(1):221-230
The notion of coorbits for spaces with quantum group actions is introduced. A space with a quantum group action is given by a pair of algebras: an associative algebra which is the analog of a classical topological space, and a Hopf algebra which is the analog of a classical topological group. The Hopf algebra acts on the associative algebra via a comodule structure mapping which is also an algebra homomorphism. For a space with a quantum group action, a coorbit is a pair of spaces given by the image and the kernel of an algebra homomorphism from the associative algebra to the Hopf algebra. The coorbits of several types of quantum homogeneous spaces are discussed. In the case when the associative algebra is the group algebra of a group and the Hopf algebra is a quotient of the group algebra, the connection between the set of coorbits and the character group is established. 相似文献
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《数学的实践与认识》2015,(14)
二元码Mq(n,d,k)是一个非适应性分组测试(NGT)算法的数学模型,是一个d-disjunct矩阵.二元码的汉明距离(Hamming)决定着码的检错性和纠错性,通过计算二元码Mq(n,d,k)的汉明距离,得到了它的检错性和纠错性. 相似文献
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The quantum algebra
in the limit q 0 is proposed as a symmetry algebra for the genetic code. The nucleotide triplets (codons) in the DNA chain are classified in crystal bases. This construction can be compared to the baryon classification from quarks in particle physics, one main difference being the natural order in the state constituents provided by the crystal base. An operator ensuring the correspondence between codons and amino acids is constructed from the above algebra: two codons corresponding to the same or different amino acids acquire the same or different eigenvalues respectively. Then a set of relations between the physicochemical properties of the amino acids are derived and compared with the experimental data. Correlations of the codon usage for quartets and sextets are determined, fitting naturally in the framework of this model. 相似文献
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We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points
Gromov–Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our main combinatorial
tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincaré duality.
In particular, we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties.
DOI: . 相似文献
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We show that the analytic rank, as defined by Murphy, of a unitalgraph C*-algebra is either 1 or 0, depending on whether or notthe underlying graph possesses an initial loop. As a corollary,we show that the analytic rank of certain quantum spaces (includingsome quantum spheres, projective spaces and lens spaces) is1. 2000 Mathematics Subject Classification 46L05, 46L65, 46L87. 相似文献
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Michael T. Anderson 《Annales Henri Poincare》2005,6(5):801-820
A new proof of Friedrich’s theorem on the existence and stability of asymptotically de Sitter spaces in 3 + 1 dimensions is
given, which extends to all even dimensions. In addition we characterize the possible limits of spaces which are globally
asymptotically de Sitter, to the past and future.
Communicated by Sergiu Klainerman
submitted 30/08/04, accepted 27/01/05 相似文献