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

In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear…

We establish $C^{1,1}$-regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly $m$-pseudoconvex manifolds, along with a variational formula for the first eigenvalue. From these results, we derive a…

Eigenvector-dependent nonlinear eigenvalue problems are considered which arise from the finite difference discretizations of the Gross-Pitaevskii equation. Existence and uniqueness of positive eigenvector for both one and two dimensional…

We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…

We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is…

In this paper, we study the first eigenvalue of a nonlinear elliptic system involving $p$-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically…

The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…

We consider the problem of finding nonzero eigenvalues and the corresponding eigenvectors of a matrix $AA^{\top}$, where $A$ is a special incidence matrix; This matrix can equivalently be defined based on a match relation between some…

An algebraic criterion that is sufficient to establish the existence of certain a priori estimates for the solution of first-order homogeneous linear characteristic problems is derived. Estimates of such kind ensure the stability of the…

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in…

The theory of eigenvalues and eigenvectors is one of the fundamental and essential components in tensor analysis. Computing the dominant eigenpair of an essentially nonnegative tensor is an important topic in tensor computation because of…

In two previous papers, we started a study of the first eigenvalue of the Dirac operator on compact spin symmetric spaces, providing, for symmetric spaces of "inner" type, a formula giving this first eigenvalue in terms of the algebraic…

In this paper we investigate homogenization results for the principal eigenvalue problem associated to $1$-homogeneous, uniformly elliptic, second-order operators. Under rather general assumptions, we prove that the principal eigenpair…

We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…

Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…

We suggest a modification of the operator exponential method for the numerical solving the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions…

We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest. We show that the calculation is greatly facilitated by the application of the discriminant to…

We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…

The main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic and homogenous. In particular we prove maximum and comparison principle, Holder…

A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is…