共查询到20条相似文献,搜索用时 921 毫秒
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The matrix with centrosymmetric structure is an important kind of structured matrices with many applications in various physics and engineering problems.The eigenvalue problem for a centrosymmetric matrix can be reduced to the other eigenvalue problems of lower order.We introduce the centrosymmetric structure to the tensor field and focus on the spectral radius of this particular tensor.Then we show that properties of centrosymmetric matrices hold true for tensors situation. 相似文献
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该文对一类广义对角占优矩阵M,给出了迭代矩阵M-1N 的谱半径的上界.特别,当M是严格对角占优时,证明了所得到的估计值总比通常用作谱半径的估计值要好. 相似文献
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In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known results about various spectral radii, including the adjacency spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance signless Laplacian spectral radius of a graph or a digraph. 相似文献
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We present an upper and a lower bound for the spectral radius of non-negative matrices. Then we give the bounds for the spectral
radius of digraphs.
Received February 10, 1999, Revised November 13, 2000, Accepted March 5, 2001 相似文献
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本文利用特征值交错方法研究了图的谱半径下界等问题,得到了图谱半径的两个新的紧下界,以及图的Laplace谱与四边形个数的一个关系式. 相似文献
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扈生彪 《纯粹数学与应用数学》2009,25(1):47-50
通过对图的最大特征分量与顶点度之间的关系的刻画,得到了图的谱半径与参数最大度和次大度之间的不等关系,进而获得了简单连通非正则图的谱半径的若干上界. 相似文献
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The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph. It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph, and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph. In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius, where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph. 相似文献
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The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds. 相似文献
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Let us consider weighted graphs, where the weights of the edges are positive definite matrices. The eigenvalues of a weighted graph are the eigenvalues of its adjacency matrix and the spectral radius of a weighted graph is also the spectral radius of its adjacency matrix. In this paper, we obtain two upper bounds for the spectral radius of weighted graphs and compare with a known upper bound. We also characterize graphs for which the upper bounds are attained. 相似文献
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Fuad Kittaneh 《Proceedings of the American Mathematical Society》2006,134(2):385-390
We prove several spectral radius inequalities for sums, products, and commutators of Hilbert space operators. Pinching inequalities for the spectral radius are also obtained.
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连通图$G$的距离无符号拉普拉斯矩阵定义为$\mathcal{Q}(G)=Tr(G)+D(G)$, 其中$Tr(G)$和$D(G)$分别为连通图$G$的点传输矩阵和距离矩阵. 图$G$的距离无符号拉普拉斯矩阵的最大特征值称为$G$的距离无符号拉普拉斯谱半径. 本文确定了给定点数的双圈图中具有最大的距离无符号拉普拉斯谱半径的图. 相似文献
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Guangbin Wang Hao WenLiangliang Li Xue Li 《Applied mathematics and computation》2011,217(18):7509-7514
In this paper, we obtain bounds for the spectral radius of the matrix lω,r which is the iterative matrix of the generalized accelerated overrelaxation (GAOR) iterative method. Moreover, we present one convergence theorem of the GAOR method. Finally, we present two numerical examples. 相似文献
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Chuan-Long Wang 《Applied mathematics and computation》2010,216(6):1687-1693
In this paper, we generalize the saddle point problem to general symmetric indefinite systems, we also present a kind of convergent splitting iterative methods for the symmetric indefinite systems. A special divergent splitting is introduced. The sufficient condition is discussed that the eigenvalues of the iteration matrix are real. The spectral radius of the iteration matrix is discussed in detail, the convergence theories of the splitting iterative methods for the symmetric indefinite systems are obtained. Finally, we present a preconditioner and discuss the eigenvalues of preconditioned matrix. 相似文献