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We prove that a linear fractional operator with an asymptotically constant lower order term in the whole space admits eigenvalues.

Analysis of PDEs · Mathematics 2015-06-19 Giacomo Bocerani , Dimitri Mugnai

Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…

Materials Science · Physics 2007-05-23 Nimal Wijesekera , Guogang Feng , Thomas L. Beck

The linearized Vlasov equation for a plasma system in a uniform magnetic field and the corresponding linear Vlasov operator are studied. The spectrum and the corresponding eigenfunctions of the Vlasov operator are found. The spectrum of…

Mathematical Physics · Physics 2009-10-31 Biao Wu

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to…

Econometrics · Economics 2024-11-20 Majid M. Al-Sadoon

It is shown that eigenvalues of Laplace-Beltrami operators on compact Riemannian manifolds can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polyharmonic functions with singularities. In…

Functional Analysis · Mathematics 2014-03-21 Isaac Z. Pesenson

Linearization is a standard method in the computation of eigenvalues and eigenvectors of matrix polynomials. In the last decade a variety of linearization methods have been developed in order to deal with algebraic structures and in order…

Numerical Analysis · Mathematics 2022-07-05 Namita Behera , Avisek Bist

We propose a multigrid correction scheme to solve a new Steklov eigenvalue problem in inverse scattering. With this scheme, solving an eigenvalue problem in a fine finite element space is reduced to solve a series of boundary value problems…

Numerical Analysis · Mathematics 2018-06-18 Yu Zhang , Hai Bi , Yidu Yang

The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…

Numerical Analysis · Mathematics 2020-03-02 Ning Zhang , Xiaole Han , Yunhui He , Hehu Xie , Chun'guang You

We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…

Numerical Analysis · Mathematics 2022-01-10 Rifqi Aziz , Emre Mengi , Matthias Voigt

In this paper we deal with an eigenvalue problem in an interface elliptic equation. We characterize the set of principal eigenvalues as a level set of a concave and regular function. As application, we study a problem arising in population…

Analysis of PDEs · Mathematics 2024-08-08 Braulio B. V. Maia , Mónica Molina-Becerra , Cristian Morales-Rodrigo , Antonio Suárez

This paper is concerned with continuous dependence of the n-th eigenvalue on self-adjoint discrete Sturm-Liouville problems. The n-th eigenvalue is considered as a function in the space of the problems. A necessary and sufficient condition…

Spectral Theory · Mathematics 2015-05-29 Hao Zhu , Yuming Shi

We treat the eigenvalue problem posed by self-similar potentials, i.e. homogeneous functions under a particular affine transformation, by means of symmetry techniques. We find that the eigenfunctions of such problems are localized, even…

Quantum Physics · Physics 2017-08-01 E. Sadurní , S. Castillo

We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear…

Classical Analysis and ODEs · Mathematics 2014-07-01 Anna Capietto , Walter Dambrosio , Duccio Papini

The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses complex contour integration to calculate the eigenvectors whose eigenvalues that are located inside some user-defined region in the complex plane. This…

Computational Physics · Physics 2018-01-31 Brendan Gavin , Agnieszka Międlar , Eric Polizzi

This paper addresses particular eigenvalue problems within the context of two quaternionic function theories. More precisely, we study two concrete classes of quaternionic eigenvalue problems, the first one for the slice derivative operator…

Complex Variables · Mathematics 2023-10-16 Rolf Sören Krausshar , Alessandro Perotti

This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…

Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…

Computational Complexity · Computer Science 2018-04-18 Aleksandr Maksimenko

We prove convergence of the Maxwell eigenvalue problem using quadratic or higher Lagrange finite elements on Worsey-Farin splits in three dimensions. To do this, we construct two Fortin-like operators to prove uniform convergence of the…

Numerical Analysis · Mathematics 2022-04-26 Daniele Boffi , Sining Gong , Johnny Guzmán , Michael Neilan

This work deals with approximate solution of generalized eigenvalue problem with coefficient matrix that is an affine function of d-parameters. The coefficient matrix is assumed to be symmetric positive definite and spectrally equivalent to…

Numerical Analysis · Mathematics 2025-03-12 Joanna Bisch , Antti Hannukainen

Consider a linear programming problem with n primal and m dual variables paired with n dual and m primal slack variables respectively, and aggregately denote these variables and slack variables as a vector z of length 2(n+m). Unlike…

Optimization and Control · Mathematics 2026-05-20 Wei Jing-Yuan