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901.
The contour integral‐based eigensolvers are the recent efforts for computing the eigenvalues inside a given region in the complex plane. The best‐known members are the Sakurai–Sugiura method, its stable version CIRR, and the FEAST algorithm. An attractive computational advantage of these methods is that they are easily parallelizable. The FEAST algorithm was developed for the generalized Hermitian eigenvalue problems. It is stable and accurate. However, it may fail when applied to non‐Hermitian problems. Recently, a dual subspace FEAST algorithm was proposed to extend the FEAST algorithm to non‐Hermitian problems. In this paper, we instead use the oblique projection technique to extend FEAST to the non‐Hermitian problems. Our approach can be summarized as follows: (a) construct a particular contour integral to form a search subspace containing the desired eigenspace and (b) use the oblique projection technique to extract desired eigenpairs with appropriately chosen test subspace. The related mathematical framework is established. Comparing to the dual subspace FEAST algorithm, we can save the computational cost roughly by a half if only the eigenvalues or the eigenvalues together with their right eigenvectors are needed. We also address some implementation issues such as how to choose a suitable starting matrix and design‐efficient stopping criteria. Numerical experiments are provided to illustrate that our method is stable and efficient. 相似文献
902.
This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u = -λu, x ∈Ω, u = 0, x ∈ (δ)Ω, where Ω (∩) Rn is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T.Yau et al. 相似文献
903.
G. Santhanam 《Proceedings Mathematical Sciences》2007,117(3):307-315
Let M be a closed hypersurface in a simply connected rank-1 symmetric space . In this paper, we give an upper bound for the first eigenvalue of the Laplacian of M in terms of the Ricci curvature of and the square of the length of the second fundamental form of the geodesic spheres with center at the center-of-mass of
M. 相似文献
904.
Thomas J. Laffey 《Linear algebra and its applications》2007,421(1):97-109
Let σ = (λ1, … , λn) be the spectrum of a nonnegative symmetric matrix A with the Perron eigenvalue λ1, a diagonal entry c and let τ = (μ1, … , μm) be the spectrum of a nonnegative symmetric matrix B with the Perron eigenvalue μ1. We show how to construct a nonnegative symmetric matrix C with the spectrum
(λ1+max{0,μ1-c},λ2,…,λn,μ2,…,μm). 相似文献
905.
A. Cañada 《Mathematische Nachrichten》2007,280(3):235-241
Let us consider the boundary‐value problem where g: ? → ? is a continuous and T ‐periodic function with zero mean value, not identically zero, (λ, a) ∈ ?2 and ∈ C [0, π ] with ∫π 0 (x) sin x dx = 0. If λ 1 denotes the first eigenvalue of the associated eigenvalue problem, we prove that if (λ, a) → (λ 1, 0), then the number of solutions increases to infinity. The proof combines Liapunov–Schmidt reduction together with a careful analysis of the oscillatory behavior of the bifurcation equation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
906.
Fa-en WU~ 《中国科学A辑(英文版)》2007,50(8):1078-1086
Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 < λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang. 相似文献
907.
Based on the theory of inverse eigenvalue problem, a correction of an approximate model is discussed, which can be formulated
as NX=XΛ, where X and Λ are given identified modal and eigenvalues matrices, respectively. The solvability conditions for a symmetric skew-Hamiltonian
matrix N are established and an explicit expression of the solutions is derived. For any estimated matrix C of the analytical model, the best approximation matrix to minimize the Frobenius norm of C − N is provided and some numerical results are presented. A perturbation analysis of the solution is also performed, which has scarcely appeared in existing literatures.
Supported by the National Natural Science Foundation of China(10571012, 10771022), the Beijing Natural Science Foundation
(1062005) and the Beijing Educational Committee Foundation (KM200411232006, KM200611232010). 相似文献
908.
Jiachang SUN Dingsheng WANG Murong JIANG Zhijie YANG RDCPS Institute of Software Chinese Academy of Sciences Beijing China e-mail: sun@mail.rdcps.ac.cn Institute of Physics Chinese Academy of Sciences Beijing China Department o 《Communications in Nonlinear Science & Numerical Simulation》2001,6(2)
Introduction Nonlinear differential eigenvalue problems are the basic ones in taledating energy function for multi-particled in Physics, chemistry and malarial science. ESpedally in computingbyronic stab~ and energy hial in the 8~ of multi-p~, "eder Of problems aretO get the panal sam Of the dedsied and energies by bang "Fact p~le". The ordinary~d, the srvcailed sdsconsistenCy aPP~, ned to ~e all or ~ of the eigenndues and eigenhations out. As the nUmber Of atoms inCreee, the computing pr… 相似文献
909.
1 IntroductionWe deal with the problem{ it:;,."--'"'::3of (11)where 9 C RN, N 2 3 is a bounded domain with smooth boundary 0fl, 0n = ro U r1, ro andYl have (N -- 1)-dinlensiollal Hausdorff nleasuret r E L'(r1), yt 2 0, V * 0 on r1, 7 denotesthe u11it outward normal and p = 2* = ee is the critical SoboleY exponent fOr the Sobolevembedding V(O) - H(O), V(fl) = {u E H'(fl) l u = 0 on ro}'The case ro and r1 have positive (N -- 1)-dimellsional Hausdoor measure aud p = 0on r1 in (1.1), has… 相似文献
910.
本文考虑非齐次Kirchhoff型方程解的存在性与多解性:m(‖u‖N)(-ΔNu+V(x)|u|N-2u)=f(x,y)/|x|β+∈h(x),x∈RN,其中N≥2,‖u‖N=fRN(|▽u|N+V(x)|u|N)dx,ΔNu=div(|▽u|N-2▽u)是N-拉普拉斯算子,m:R+→R+表示Kirchhoff函数,... 相似文献