The implicitly restarted Arnoldi method implicitly applies a polynomial lter to the Arnoldi vectors by use of orthogonal transformations. In this paper, an implicit ltering by rational functions is proposed for the rational Krylov method. This ltering is performed in an eecient way. Two applications are considered. The rst one is the ltering of unwanted eigenvalues using exact shifts. This appr...

Abstract. We consider semilinear eigenvalue problems for hemivariational inequalities at resonance. First we consider problems which are at resonance in a higher eigenvalue $\lambda_{k}$ (with $k\geq 1$ ) and prove two multiplicity theorems asserting the existence of at least $k$ pairs of nontrivial solutions. Then we consider problems which are resonant at the first eigenvalue $\lambda_{1}>0$ ...

Motivated by problems involving diffusion through small gaps, we revisit twodimensional eigenvalue problems with localized perturbations to Neumann boundary conditions. We recover the known result that the gravest eigenvalue is O(jln ej), where e is the ratio of the size of the hole to the length-scale of the domain, and provide a simple and constructive approach for summing the inverse logarit...

We present a novel multitask learning framework called multitask generalized eigenvalue program (MTGEP), which jointly solves multiple related generalized eigenvalue problems (GEPs). This framework is quite general and can be applied to many eigenvalue problems in machine learning and pattern recognition, ranging from supervised learning to unsupervised learning, such as principal component ana...

the sharp upper bounds and the sharp lower bounds of the largest eigenvalues $lambda_1$, the least eigenvalue $lambda_n$, the second largest eigenvalue $lambda_2$, the spread and the separator among all firefly graphs on $n$ vertices are determined.

time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. the stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. it is well-known that the stabi...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

We present a new computational approach for a class of large-scale nonlinear eigenvalue problems (NEPs) that are nonlinear in the eigenvalue. The contribution of this paper is two-fold. We derive a new iterative algorithm for NEPs, the tensor infinite Arnoldi method (TIAR), which is applicable to a general class of NEPs, and we show how to specialize the algorithm to a specific NEP: the wavegui...

The power of density functional theory is often limited by the high computational demand in solving an eigenvalue problem at each self-consistent-field (SCF) iteration. The method presented in this paper replaces the explicit eigenvalue calculations by an approximation of the wanted invariant subspace, obtained with the help of well-selected Chebyshev polynomial filters. In this approach, only ...

This publication is a contribution to basic research in image comparison using eigenvalue spectra as features. The differential-geometric approach of eigenvalue spectrum based descriptors is naturally applicable to shape data, but so far little work has been done to transfer it to the setting of image data painted on a rectangle or general curved surface. We present a new semi-global feature de...