相关论文: Computing the first eigenpair for problems with va…

The explicit solution of the initial-values problem is exhibited of a subclass of the autonomous system of 2 coupled first-order ODE s with second-degree polynomial right-hand sides, hence featuring 12 a prior arbitrary (time-independent)…

We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want…

The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…

We compute the exact value of the squared condition number for the polynomial eigenvalue problem, when the input matrices have entries coming from the standard complex Gaussian distribution, showing that in general this problem is quite…

We estimate the number of integer solutions to decomposable form inequalities (both asymptotic estimates and upper bounds are provided) when the degree of the form and the number of variables are relatively prime. These estimates display…

For standard eigenvalue problems, a closed-form expression for the condition numbers of a multiple eigenvalue is known. In particular, they are uniformly 1 in the Hermitian case, and generally take different values in the non-Hermitian…

This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…

We prove a comparison theorem on the first Neumann eigenvalue on Bakry-Emery manifolds. Examples are constructed to illustrate the sharpness of the result. A linear explicit lower bound is also proved. We also discuss the asymptotic…

Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…

It is known (see e.g. [2], [4], [5], [6]) that continuous variations in the entries of a complex square matrix induce continuous variations in its eigenvalues. If such a variation arises from one real parameter $\alpha \in [0, 1]$, then the…

In this paper, the concepts of Pareto $H$-eigenvalue and Pareto $Z$-eigenvalue are introduced for studying constrained minimization problem and the necessary and sufficient conditions of such eigenvalues are given. It is proved that a…

We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such…

We consider the buckling eigenvalue problem for a clamped plate in the annulus. We identify the first eigenvalue in dependence of the inner radius, and study the number of nodal domains of the corresponding eigenfunctions. Moreover, in…

We derive a second order estimate for the first m eigenvalues and eigenfunctions of the linearized Gel'fand problem associated to solutions which blow-up at m points. This allows us to determine, in some suitable situations, some…

We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at…

The reliability is of the most importance when employing a numerical method to solve the eigenvalue integral equations. In this paper, we present one type of particular singularities (pseudosingularities) existing in eigenvalue integral…

We consider the inverse spectral theory of vibrating string equations. In this regard, first eigenvalue Ambarzumyan-type uniqueness theorems are stated and proved subject to separated, self-adjoint boundary conditions. More precisely, it is…

In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters $\omega$ and we are interested in the…

Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &\Delta {\mathbf u}+ \alpha{\rm grad}(\text{div}{\mathbf…

Let $1 \leq m \leq n$ be two integers and $\Omega \Subset \C^n$ a bounded $m$-hyperconvex domain in $\C^n$. Using a variational approach, we prove the existence of the first eigenvalue and an associated eigenfunction which is…