Related papers: Computation of Eigenvalues for Nonlocal Models by …
A new technique for approximating eigenvalues and eigenvectors of a self-adjoint operator is presented. The method does not incur spectral pollution, uses trial spaces from the form domain, has a self-adjoint algorithm, and exhibits…
We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication…
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an inverse eigenvalue problem, which can be solved using…
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…
How do the geometric properties of a domain impact the spectrum of an operator defined on it? How do we compute accurate and reliable approximations of these spectra? The former question is studied in spectral geometry, and the latter is a…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
We study location of eigenvalues of one-dimensional discrete Schr\"odinger operators with complex $\ell^{p}$-potentials for $1\leq p\leq \infty$. In the case of $\ell^{1}$-potentials, the derived bound is shown to be optimal. For $p>1$, two…
The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based…
We derive new estimates for distances between optimal matchings of eigenvalues of non-normal matrices in terms of the norm of their difference. We introduce and estimate a hyperbolic metric analogue of the classical spectral-variation…
New estimates for eigenvalues of non-self-adjoint multi-dimensional Schr\"{o}dinger operators are obtained in terms of $L_{p}$-norms of the potentials. The results extend and improve those obtained previously. In particular, diverse…
Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations $\mathcal L u = f$. The framework posits the existence of a left-Fredholm regulator for $\mathcal L$ and the…
Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…
We study resolvent estimates for non-selfadjoint semiclassical pseudodifferential operators with double characteristics. Assuming that the quadratic approximation along the double characteristics is elliptic, we obtain polynomial upper…
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…
We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation with Ince symbol…
In this article, the existence of the spectrum (the eigenvalues) for the nonlinear continuous operators acting in the Banach spaces is investigated. For the study, this question is used a different approach that allows the studying of all…
Forecasting water content dynamics in heterogeneous porous media has significant interest in hydrological applications; in particular, the treatment of infiltration when in presence of cracks and fractures can be accomplished resorting to…
We study the spectral theory of mixed local and nonlocal operators with lower-order terms in the right-hand side of the equation. This kind of problems is motivated by the analysis of superposition operators of mixed order and with the…
We present a spectral method for one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, including ones with irrational order, multiple fractional orders,…