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排序方式: 共有299条查询结果,搜索用时 31 毫秒
31.
Bijaya Laxmi Panigrahi Gnaneshwar Nelakanti 《Journal of Computational and Applied Mathematics》2011,235(8):2380-2391
In this paper, we consider the Galerkin and collocation methods for the eigenvalue problem of a compact integral operator with a smooth kernel using the Legendre polynomials of degree ≤n. We prove that the error bounds for eigenvalues are of the order O(n−2r) and the gap between the spectral subspaces are of the orders O(n−r) in L2-norm and O(n1/2−r) in the infinity norm, where r denotes the smoothness of the kernel. By iterating the eigenvectors we show that the iterated eigenvectors converge with the orders of convergence O(n−2r) in both L2-norm and infinity norm. We illustrate our results with numerical examples. 相似文献
32.
Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let λ be an eigenvalue of A with multiplicity mA(λ). An edge e=ij is said to be Parter (resp., neutral, downer) for λ,A if mA(λ)−mA−e(λ) is negative (resp., 0, positive ), where A−e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue λ of A, if |S|=mA(λ) and A−S has no eigenvalue λ. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is proved. We prove that neutral edges always exist for eigenvalues of multiplicity more than 1. It is also proved that an edge e=uv is a downer edge for λ,A if and only if u and v are both downer vertices for λ,A; and e=uv is a neutral edge if u and v are neutral vertices. Among other results, it is shown that any edge star set for each eigenvalue of a tree is a matching. 相似文献
33.
Let Q be a bounded open domain in R^n with smooth boundaryаΩ.Let X=(X1,X2…,Xm)be a system of general Grushin type vector fields defined onΩand the boundaryаΩis non-characteristic for X.For△x=∑j=1^mXj^2,we denoteλk as the k-th eigenvalue for the bi-subelliptic operator△X2^2 onΩ.In this paper,by using the sharp sub-elliptic estimates and maximally hypoeliptic estimates,we give the optimal lower bound estimates ofλk for the operatork△X^2. 相似文献
34.
Andr Goldman Pierre Calka 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2003,39(6):90-1082
Denote by (t)=∑n1e−λnt, t>0, the spectral function related to the Dirichlet Laplacian for the typical cell
of a standard Poisson–Voronoi tessellation in
. We show that the expectation E(t), t>0, is a functional of the convex hull of a standard d-dimensional Brownian bridge. This enables us to study the asymptotic behaviour of E(t), when t→0+,+∞. In particular, we prove that the law of the first eigenvalue λ1 of
satisfies the asymptotic relation lnP{λ1t}−2dωdj(d−2)/2d·t−d/2 when t→0+, where ωd and j(d−2)/2 are respectively the Lebesgue measure of the unit ball in
and the first zero of the Bessel function J(d−2)/2. 相似文献
35.
A graph is singular of nullity η if zero is an eigenvalue of its adjacency matrix with multiplicity η. If η(G)=1, then the core of G is the subgraph induced by the vertices associated with the non-zero entries of the zero-eigenvector. A connected subgraph of G with the least number of vertices and edges, that has nullity one and the same core as G, is called a minimal configuration. A subdivision of a graph G is obtained by inserting a vertex on every edge of G. We review various properties of minimal configurations. In particular, we show that a minimal configuration is a tree if and only if it is a subdivision of some other tree. 相似文献
36.
Gene H. Golub Richard Underwood 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1970,21(3):318-326
Sommario SiaA una matrice reale simmetrica di ordinen, B una matrice reale simmetrica di ordinen per cuix
T
B
x>0 eC una matricen×p di rangor conrp. Si vogliono deteminare i vettorix per cui, JIMELè stazionaria eC
T
x= è il vettore nullo. È dato un algoritmo per generare un autosistema simmetrico i cui autovalori sono i valori stazionarì e per determinare i vettorix. Sono altresì presentate parecchie applicazioni dell'algoritmo.
Dedicated to Professor L. Collatz on his sixtieth birthday
This author was in part supported by the Atomic Energy Commission. 相似文献
Dedicated to Professor L. Collatz on his sixtieth birthday
This author was in part supported by the Atomic Energy Commission. 相似文献
37.
Ruyun Ma 《Journal of Mathematical Analysis and Applications》2006,314(1):254-265
We consider boundary value problems of fourth-order differential equations of the form
38.
Higher-order asymptotic formula for the eigenvalues of Sturm-Liouville problem with n turning points
In this paper, we investigate the asymptotic behavior of the differential equation
39.
Thomas Kühn Mieczys?aw Masty?o 《Journal of Mathematical Analysis and Applications》2010,369(1):408-1265
We estimate Weyl numbers and eigenvalues of operators via studying their abstract summing norms. In particular we prove estimates of these summing norms for abstract interpolation Lorentz spaces. For this we combine factorization theorems with estimates of concavity constants. Finally we apply our general eigenvalue results to integral operators with kernels of weakly singular type. We obtain asymptotically optimal estimates which extend the well-known classical results. 相似文献
40.
We present a new matrix-free method for the computation of negative curvature directions based on the eigenstructure of minimal-memory BFGS matrices. We determine via simple formulas the eigenvalues of these matrices and we compute the desirable eigenvectors by explicit forms. Consequently, a negative curvature direction is computed in such a way that avoids the storage and the factorization of any matrix. We propose a modification of the L-BFGS method in which no information is kept from old iterations, so that memory requirements are minimal. The proposed algorithm incorporates a curvilinear path and a linesearch procedure, which combines two search directions; a memoryless quasi-Newton direction and a direction of negative curvature. Results of numerical experiments for large scale problems are also presented. 相似文献