Related papers: From eigenvector nonlinearities with quadratic str…
We discuss a quartic eigenvalue problem arising in the context of an optical waveguiding problem involving atomically thick 2D materials. The waveguide configuration we consider consists of a gradient-index (spatially dependent) dielectric…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
A special class of symmetry reductions called nonclassical equivalence transformations is discussed in connection to a class of parameter identification problems represented by partial differential equations. These symmetry reductions…
We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of…
A numerical algorithm is proposed to deal with parametric eigenvalue problems involving non-Hermitian matrices and is exploited to find location of defective eigenvalues in the parameter space of non-Hermitian parametric eigenvalue…
In this work we present a framework for studying the eigenvalues of a family of matrices with a particular displacement structure. The family admits a specific decomposition as the product of an upper and a lower triangular matrices having…
In this paper, we propose a method for computing eigenvalues of elliptic problems using Deep Learning techniques. A key feature of our approach is that it is independent of the space dimension and can compute arbitrary eigenvalues without…
We present a novel, global algorithm for solving polynomial multiparameter eigenvalue problems (PMEPs) by leveraging a hidden variable tensor Dixon resultant framework. Our method transforms a PMEP into one or more univariate polynomial…
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…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
We consider time-harmonic scalar transmission problems between dielectric and dispersive materials with generalized Lorentz frequency laws. For certain frequency ranges such equations involve a sign-change in their principle part. Due to…
We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints.…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
In this paper we study polynomial maps of vector spaces and their eigenvectors and eigenvalues. The new quantity called complanart is defined. Complanarts determine complanarity of solution vectors of systems of polynomial equations.…
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution…
A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…
In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown…
We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional…