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

While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…

In this paper we propose a homotopy method to compute the largest eigenvalue and a corresponding eigenvector of a nonnegative tensor. We prove that it converges to the desired eigenpair when the tensor is irreducible. We also implement the…

In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…

In this note we study the eigenvalue problem for a quadratic form associated with Strichartz estimates for the Schr\"{o}dinger equation, proving in particular a sharp Strichartz inequality for the case of odd initial data. We also describe…

Recently, the eigenvalue problems formulated with symmetric positive definite bilinear forms have been well investigated with the aim of explicit bounds for the eigenvalues. In this paper, the existing theorems for bounding eigenvalues are…

We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplace's operator inside a domain containing a cloud of small rigid inclusions. The separation of the small inclusions is characterised by…

We review the theory of first BGG operators and study how to approach them and find their solution on homogeneous geometries. We provide many new examples of parabolic geometries that admit solutions of first BGG operators with many…

We consider generalized operator eigenvalue problems in variational form with random perturbations in the bilinear forms. This setting is motivated by variational forms of partial differential equations with random input data. The…

This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…

Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions…

The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous…

In this paper, we study optimization of the first eigenvalue of the heat equation with spatially nonuniform conductivity on a bounded domain under several constraints for the conductivity. We consider this problem in various boundary…

We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires…

We investigate the problem of the existence of first integrals for multidimensional and ordinary linear differential systems with constant coefficients. The spectral method of the first integrals basis construction for these systems of…

In this paper, we are concerned with the first initial boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds. As usual, the establishment of the a priori C^2 estimates is our main part. Based on…

In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…

In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new…

Eigenvalue problems arise in many areas of physics, from solving a classical electromagnetic problem to calculating the quantum bound states of the hydrogen atom. In textbooks, eigenvalue problems are defined for linear problems,…

Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…

In this short communication we introduce a rather simple autonomous system of 2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose initial-values problem is explicitly solvable by algebraic operations. Its ODEs…