共查询到20条相似文献,搜索用时 31 毫秒
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Equilibria in mechanics or in transportation models are not always expressed through a system of equations, but sometimes they are characterized by means of complementarity conditions involving a convex cone. This work deals with the analysis of cone-constrained eigenvalue problems. We discuss some theoretical issues like, for instance, the estimation of the maximal number of eigenvalues in a cone-constrained problem. Special attention is paid to the Paretian case. As a short addition to the theoretical part, we introduce and study two algorithms for solving numerically such type of eigenvalue problems. 相似文献
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The possibilities for a graph onn vertices with spectrum >>– and some vertex of valencen–1 are presented. Some of these are constructed. 相似文献
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In this paper,we study large m asymptotics of the l 1 minimal m-partition problem for the Dirichlet eigenvalue.For any smooth domainΩ?Rnsuch that|Ω|=1,we prove that the limit limm→∞l1m(Ω)=c 0 exists,and the constant c 0 is independent of the shape ofΩ.Here,l1m(Ω)denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any m-partition ofΩ. 相似文献
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Generalized eigenvalue problems can be considered as a system of polynomials. The homotopy continuation method is used to find all the isolated zeros of the polynomial system which corresponds to the eigenpairs of the generalized eigenvalue problem. A special homotopy is constructed in such a way that there are exactly n distinct smooth curves connecting trivial solutions to desired eigenpairs. Since the curves followed by general homotopy curve following scheme are computed independently of one another, the algorithm is a likely candidate for exploiting the advantages of parallel processing to the generalized eigenvalue problems. 相似文献
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Based on a linear finite element space,two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed.Some relationships between the finite element method and the finite difference method are addressed,too. 相似文献
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We propose a Jacobi–Davidson type method to compute selected eigenpairs of the product eigenvalue problem Am?A1x=λx, where the matrices may be large and sparse. To avoid difficulties caused by a high condition number of the product matrix, we split up the action of the product matrix and work with several search spaces. We generalize the Jacobi–Davidson correction equation and the harmonic and refined extraction for the product eigenvalue problem. Numerical experiments indicate that the method can be used to compute eigenvalues of product matrices with extremely high condition numbers. 相似文献
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Bruno Sévennec 《Mathematische Annalen》2002,324(1):195-211
We improve – roughly by a factor 2 – the known bound on the multiplicity of the second eigenvalue of Schr?dinger operators
(i.e. Laplace plus potential) on closed surfaces. This gives four new topological types of surfaces for which Colin de Verdière's
conjecture relating the maximal multiplicity to the chromatic number of the surface is verified. The proof goes by defining
a space of "nodal splittings” of the surface, equipped with a double covering to which a Borsuk-Ulam type theorem is applied.
Received: 19 June 2001; revised version: 18 March 2002 /Published online: 17 June 2002 相似文献
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Gregoire Nadin 《Annali di Matematica Pura ed Applicata》2009,188(2):269-295
This paper deals with the generalized principal eigenvalue of the parabolic operator , where the coefficients are periodic in t and x. We give the definition of this eigenvalue and we prove that it can be approximated by a sequence of principal eigenvalues
associated to the same operator in a bounded domain, with periodicity in time and Dirichlet boundary conditions in space.
Next, we define a family of periodic principal eigenvalues associated with the operator and use it to give a characterization
of the generalized principal eigenvalue. Finally, we study the dependence of all these eigenvalues with respect to the coefficients.
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Tian-fei WANG Department of Mathematics Leshan Teachers College Leshan China 《中国科学A辑(英文版)》2007,50(12):1755-1764
Let K be the quasi-Laplacian matrix of a graph G and B be the adjacency matrix of the line graph of G,respectively.In this paper,we first present two sharp upper bounds for the largest Laplacian eigenvalue of G by applying the non-negative matrix theory to the similar matrix D~(-1/2) KD~(1/2) and U~(-1/2)BU~(1/2),respectively,where D is the degree diagonal matrix of G and U=diag(d_u,d_v,:uv∈E(G)). And then we give another type of the upper bound in terms of the degree of the vertex and the edge number of G.Moreover,we determine all extremal graphs which achieve these upper bounds.Finally, some examples are given to illustrate that our results are better than the earlier and recent ones in some sense. 相似文献
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Summary The computation of the smallest positive eigenvalue
* of a quadratic -matrix is used to determine the stability of structures. In addition to existence results we derive two efficient and reliable methods to calculate
*. Both methods are based on shift techniques which are discussed thoroughly with respect to convergence. 相似文献
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We present a new implementation of the two-grid method for computing extremum eigenpairs of self-adjoint partial differential operators with periodic boundary conditions. A novel two-grid centered difference method is proposed for the numerical solutions of the nonlinear Schrödinger–Poisson (SP) eigenvalue problem.We solve the Poisson equation to obtain the nonlinear potential for the nonlinear Schrödinger eigenvalue problem, and use the block Lanczos method to compute the first k eigenpairs of the Schrödinger eigenvalue problem until they converge on the coarse grid. Then we perform a few conjugate gradient iterations to solve each symmetric positive definite linear system for the approximate eigenvector on the fine grid. The Rayleigh quotient iteration is exploited to improve the accuracy of the eigenpairs on the fine grid. Our numerical results show how the first few eigenpairs of the Schrödinger eigenvalue problem are affected by the dopant in the Schrödinger–Poisson (SP) system. Moreover, the convergence rate of eigenvalue computations on the fine grid is O(h3). 相似文献
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Kumar Dookhitram Ravindra Boojhawon Ashvin Gopaul Muddun Bhuruth 《Numerical Algorithms》2011,56(4):481-495
Convergence of the implicitly restarted Arnoldi (IRA) method for nonsymmetric eigenvalue problems has often been studied by
deriving bounds for the angle between a desired eigenvector and the Krylov projection subspace. Bounds for residual norms
of approximate eigenvectors have been less studied and this paper derives a new a-posteriori residual bound for nonsymmetric
matrices with simple eigenvalues. The residual vector is shown to be a linear combination of exact eigenvectors and a residual
bound is obtained as the sum of the magnitudes of the coefficients of the eigenvectors. We numerically illustrate that the
convergence of the residual norm to zero is governed by a scalar term, namely the last element of the wanted eigenvector of
the projected matrix. Both cases of convergence and non-convergence are illustrated and this validates our theoretical results.
We derive an analogous result for implicitly restarted refined Arnoldi (IRRA) and for this algorithm, we numerically illustrate
that convergence is governed by two scalar terms appearing in the linear combination which drives the residual norm to zero.
We provide a set of numerical results that validate the residual bounds for both variants of Arnoldi methods. 相似文献