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51.
Joaquim J. Júdice Hanif D. Sherali Isabel M. Ribeiro 《Computational Optimization and Applications》2007,37(2):139-156
In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact
problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming
Problem with Complementarity Constraints and a Global Optimization Problem. A finite Reformulation–Linearization Technique
(Rlt)-based tree search algorithm is introduced for processing the EiCP via the lattermost of these formulations. Computational
experience is included to highlight the efficacy of the above formulations and corresponding techniques for the solution of
the EiCP. 相似文献
52.
Wei Chen 《Numerical Methods for Partial Differential Equations》2005,21(3):512-520
Using the technique of eigenvalue error expansion and the technique of integral identities, we derive higher order convergence rate of the eigenvalue approximation for the biharmonic eigenvalue problem based on the Ciarlet‐Raviart discretization. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
53.
We present a practical approach to Anstreicher and Lee’s masked spectral bound for maximum-entropy sampling, and we describe
favorable results that we have obtained with a Branch-and-Bound algorithm based on our approach. By representing masks in
factored form, we are able to easily satisfy a semidefiniteness constraint. Moreover, this representation allows us to restrict
the rank of the mask as a means for attempting to practically incorporate second-order information.
Supported in part by NSF Grant CCR-0203426. 相似文献
54.
Ding Qing 《数学年刊B辑(英文版)》1994,15(1):35-42
This paper establishes a new Laplacian comparison theorem which is specially useful to the manifolds of nonpositive curvature.It leads naturally to the corresponding heat kernel comparison and eigenvalue comparison theorems. Furthermore, a lower estimate of L^2-spectrum of an n-dimensional non-compact complete Cartan-Hadamard manifold is given by (n-1)k/4,provided its Ricci curvature ≤-(n-1)k(k=const.≥0). 相似文献
55.
When solving linear algebraic equations with large and sparse coefficient matrices, arising, for instance, from the discretization of partial differential equations, it is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme. Incomplete factorizations and sparse approximate inverses can provide efficient preconditioning methods but their existence and convergence theory is based mostly on M-matrices (H-matrices). In some application areas, however, the arising coefficient matrices are not H-matrices. This is the case, for instance, when higher-order finite element approximations are used, which is typical for structural mechanics problems. We show that modification of a symmetric, positive definite matrix by reduction of positive offdiagonal entries and diagonal compensation of them leads to an M-matrix. This diagonally compensated reduction can take place in the whole matrix or only at the current pivot block in a recursive incomplete factorization method. Applications for constructing preconditioning matrices for finite element matrices are described. 相似文献
56.
Ravindra K. Bisht 《Numerical Functional Analysis & Optimization》2017,38(11):1446-1457
In this paper, we propose some su?cient conditions to obtain the existence of common fixed points for a pair of self-mappings satisfying Lipschitz-type conditions in noncomplete metric space. Our results improve and extend the results of Pant [Common fixed points of Lipschitz-type mapping pairs, J. Math. Anal. Appl. 240, (1999), 280–283] and Khan et al. [Coincidences of Lipschitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9–10), (2007), 1165–1177]. As an application of our results we solve an eigenvalue problem for operators defined on a normed space. 相似文献
57.
Pin-jointed structures are first classified to trusses, tensile structures, and tensegrity structures in view of their respective stability properties. A sufficient condition for stability of an equilibrium state is derived for tensegrity structures. The condition is based on the bilinear forms of the linear and geometrical stiffness matrices considering the flexibility of members. The stability is defined by the positive definiteness of the tangent stiffness matrix, whereas the definition of prestress-stability is based on the geometrical stiffness matrix and the infinitesimal mechanisms. Numerical examples verify that the so-called super-stability condition might not be satisfied by a stable tensegrity structure, and that a prestress-stable structure can be unstable if the prestresses are moderately large. 相似文献
58.
Marina Yu. Planida 《Comptes Rendus Mecanique》2003,331(8):531-536
We consider the eigenvalue problem for the Laplace operator in a bounded three-dimensional domain where a thin tube is cut out. Imposing a Neumann boundary condition on the boundary of this tube, we construct asymptotics for eigenvalues on the small parameter that is a diameter of the tube. To cite this article: M.Yu. Planida, C. R. Mecanique 331 (2003). 相似文献
59.
Asma Hassannezhad 《Journal of Functional Analysis》2011,261(12):3419-3436
In this paper, we find upper bounds for the eigenvalues of the Laplacian in the conformal class of a compact Riemannian manifold (M,g). These upper bounds depend only on the dimension and a conformal invariant that we call “min-conformal volume”. Asymptotically, these bounds are consistent with the Weyl law and improve previous results by Korevaar and Yang and Yau. The proof relies on the construction of a suitable family of disjoint domains providing supports for a family of test functions. This method is interesting for itself and powerful. As a further application of the method we obtain an upper bound for the eigenvalues of the Steklov problem in a domain with C1 boundary in a complete Riemannian manifold in terms of the isoperimetric ratio of the domain and the conformal invariant that we introduce. 相似文献
60.
In this paper, inverse spectra problems for a differential pencil are studied. By using the approach similar to those in Hochstadt and Lieberman (1978) [14] and Ramm (2000) [26], we prove that (1) if p(x) (or q(x)) is full given on the interval [0,π], then a set of values of eigenfunctions at the mid-point of the interval [0,π] and one spectrum suffice to determine q(x) (or p(x)) on the interval [0,π] and all parameters in the boundary conditions; (2) if p(x) (or q(x)) is full given on the interval [0,π], then some information on eigenfunctions at some internal point and parts of two spectra suffice to determine q(x) (or p(x)) on the interval [0,π] and all parameters in the boundary conditions. 相似文献