共查询到20条相似文献,搜索用时 109 毫秒
1.
Uriel G. Rothblum 《Linear algebra and its applications》1975,12(3):281-292
The Perron-Frobenius theory for square, irreducible, nonnegative matrices is generalized by studying the structure of the algebraic eigenspace of an arbitrary square nonnegative matrix corresponding to its spectral radius. We give a constructive proof that this subspace is spanned by a set of semipositive vectors and give a combinatorial characterization of both the index of the spectral radius and dimension of the algebraic eigenspace corresponding to the spectral radius. This involves a detailed study of the standard block triangular representation of nonnegative matrices by giving special attention to those blocks on the diagonal having the same spectral radius as the original matrix. We also show that the algebraic eigenspace corresponding to the spectral radius contains a semipositive vector having the largest set of positive coordinates among all vectors in this subspace. 相似文献
2.
Tibor Fiala 《Numerische Mathematik》1990,57(1):473-479
Summary The Meijerink, van der Vorst type incomplete decomposition uses a position set, where the factors must be zero, but their product may differ from the original matrix. The smaller this position set is, the more the product of incomplete factors resembles the original matrix. The aim of this paper is to discuss this type of monotonity. It is shown using the Perron Frobenius theory of nonnegative matrices, that the spectral radius of the iteration matrix is a monotone function of the position set. On the other hand no matrix norm of the iteration matrix depends monotonically on the position set. Comparison is made with the modified incomplete factorization technique. 相似文献
3.
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
4.
We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results. 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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LI Kaican~ 《中国科学A辑(英文版)》2005,48(10):1430-1439
Based on the convergence rate defined by the Pearson-χ~2 distance,this pa- per discusses properties of different Gibbs sampling schemes.Under a set of regularity conditions,it is proved in this paper that the rate of convergence on systematic scan Gibbs samplers is the norm of a forward operator.We also discuss that the collapsed Gibbs sam- pler has a faster convergence rate than the systematic scan Gibbs sampler as proposed by Liu et al.Based on the definition of convergence rate of the Pearson-χ~2 distance, this paper proved this result quantitatively.According to Theorem 2,we also proved that the convergence rate defined with the spectral radius of matrix by Robert and Shau is equivalent to the corresponding radius of the forward operator. 相似文献
9.
Masatoshi Ikeuchi Hiroshi Kobayashi Hideo Sawami Hiroshi Niki 《Journal of Computational and Applied Mathematics》1979,5(4):247-258
The spectral radius of the Jacobi iteration matrix plays an important role to estimate the optimum relaxation factor, when the successive overrelaxation (SOR) method is used for solving a linear system. The specific systems are finite difference forms of the Laplace equation satisfied on a rectanglar region with two different media. Though the potential function for the inhomogeneous closed region is continuous, the first order derivative is not continuous. So this requires internal boundary conditions or interface conditions. In this paper, the spectral radius of the Jacobi iteration matrix for the inhomogeneous rectangular region is formulated and the approximation for the explicit formula, suitable for the computation of the spectral radius, is deduced. It is also found by the proposed formula that the spectral radius and the optimum relaxation factor rigorously depend on the inhomogeneity or the internal boundary conditions in the closed region, and especially vary with the position of the internal boundary. These findings are also confirmed by the numerical results of the power method.The stationary iterative method using the proposed formula for calculating estimates of the spectral radius of the Jacobi iteration matrix is compared with Carré's method, Kulstrud's method and the stationary iterative method using Frankel's theoretical formula, all for the case of some numerical models with two different media. According to the results our stationary iterative method gives the best results ffor the estimate of the spectral radius of the Jacobi iteration matrix, for the required number of iterations to calculate solutions, and for the accuracy of the solutions.As a numerical example the microstrip transmission line is taken, the propating mode of which can be approximated by a TEM mode. The cross section includes inhomogeneous media and a strip conductor. Upper and lower bounds of the spectral radius of the Jacobi iteration matrix are estimated. Our method using these estimates is also compared with the other methods. The upper bound of the spectral radius of the Jacobi iteration matrix for more general closed regions with two different media might be given by the proposed formula. 相似文献
10.
We consider the minimum spectral radius for an n×n matrix of 0's and 1's having a specified number τ of 0's. We determine this minimum spectral radius when τ⩽⌊n/2⌋⌈n/2⌉, and bound it between two consecutive integers for all other values of τ. 相似文献
11.
Manuel Pinto 《Applied mathematics and computation》2010,217(8):4167-4177
The existence and global exponential stability of an almost periodic solution of an impulsive neural network model with distributed delays is considered in a matrix setting. The approach transforms the original network into a matrix analysis problem, where a set of sufficient conditions based on spectral radius is presented. A concrete Hopfield model shows the advantages in comparison with a classical norm approach. 相似文献
12.
Nylen and Rodman [NR] introduced the notion of spectral radius property in Banach algebras in order to generalize a classical theorem of Yamamoto on the asymptotic behaviour of the singular values of ann xn matrix. In this paper we prove a conjecture of theirs in the affirmative, namely that any unital Banach algebra has the spectral radius property. In fact a slightly more general spectral property holds. We show that for every element which has spectral points which are not of finite multiplicity, the essential spectral radius is the supremum of the set of absolute values of the spectral points that are not of finite multiplicity. 相似文献
13.
The signless Laplacian spectral radius of a graph G is the largest eigenvalue of its signless Laplacian matrix. In this paper, the first four smallest values of the signless Laplacian spectral radius among all connected graphs with maximum clique of size greater than or equal to 2 are obtained. 相似文献
14.
One common problem in spectral graph theory is to determine which graphs, under some prescribed constraints, maximize or minimize the spectral radius of the adjacency matrix. Here we consider minimizers in the set of bidegreed, or biregular, graphs with pendant vertices and given degree sequence. In this setting, we consider a particular graph perturbation whose effect is to decrease the spectral radius. Hence we restrict the structure of minimizers for k-cyclic degree sequences. 相似文献
15.
The spectral radiuses of Galton-Watson branching processes which describes the speed of the process escaping from any state are calculated.Under the condition of irreducibility,it is show that this is equal to the spectral radius of Jacobi matrix of its generating function. 相似文献
16.
Xu Qunfan Zhao Minzhi Ying Jiangang 《高校应用数学学报(英文版)》2006,21(1):79-86
§1IntroductionSuppose that(X,Px)is a Markov chain on a countable(or finite)state space E.Givenany x,y∈E,we say that y can be reached from x and write x y,if there is n≥1suchthat Px(Xn=y)>0.If x y and y z,then x z.The markov chain X is said to beirreducible if any two states can be reached from each other.(See[1]or[2]).If X isirreducible,then there is a number r,with0≤r≤1,such that lim supn→∞[Px(Xn=y)]n1=r forany x,y∈E.The number r is called the spectral radius of X(refer to[3]).… 相似文献
17.
Guiding Gu 《计算数学(英文版)》2011,29(4):441-457
In this paper, a complex parameter is employed in the Hermitian and skew-Hermitian splitting (HSS) method (Bai, Golub and Ng: SIAM J. Matrix Anal. Appl., 24(2003), 603-626) for solving the complex linear system $Ax=f$. The convergence of the resulting method is proved when the spectrum of the matrix $A$ lie in the right upper (or lower) part of the complex plane. We also derive an upper bound of the spectral radius of the HSS iteration matrix, and an estimated optimal parameter $α$(denoted by $α_{est}$) of this upper bound is presented. Numerical experiments on two modified model problems show that the HSS method with $α_{est}$has a smaller spectral radius than that with the real parameter which minimizes the corresponding upper bound. In particular, for the 'dominant' imaginary part of the matrix $A$, this improvement is considerable. We also test the GMRES method preconditioned by the HSS preconditioning matrix with our parameter $α_{est}$. 相似文献
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In this paper, we present a sharp version of Bauer–Fike’s theorem. We replace the matrix norm with its spectral radius or sign-complex spectral radius for diagonalizable matrices; 1-norm and ∞-norm for non-diagonalizable matrices. We also give the applications to the pole placement problem and the singular system. 相似文献
20.
Lingsheng Shi 《Linear algebra and its applications》2007,422(1):58-66
The spectral radius of a (directed) graph is the largest eigenvalue of adjacency matrix of the (directed) graph. We give the relation on the characteristic polynomials of a directed graph and its line graph, and obtain sharp bounds on the spectral radius of directed graphs. We also give the relation on the spectral radii of a graph and its line graph. As a consequence, the spectral radius of a connected graph does not exceed that of its line graph except that the graph is a path. 相似文献