Related papers: A Contour-integral Based QZ Algorithm for Generali…
It is needed to solve generalized eigenvalue problems (GEP) in many applications, such as the numerical simulation of vibration analysis, quantum mechanics, electronic structure, etc. The subspace iteration is a kind of widely used…
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…
This work presents a novel approach to compute the eigenvalues of non-Hermitian matrices using an enhanced shifted QR algorithm. The existing QR algorithms fail to converge early in the case of non-hermitian matrices, and our approach shows…
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…
A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed curve is presented. It is based on the application of the residual theorem. The quadrature is performed by evaluating the principal argument…
This paper is to give a new understanding and applications of the subspace projection method for selfadjoint eigenvalue problems. A new error estimate in the energy norm, which is induced by the stiff matrix, of the subspace projection…
Eigenvalue problems have a distinctive forward-inverse structure and are fundamental to characterizing a system's thermal response, stability, and natural modes. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative for…
We propose an efficient computational method for evaluating the self-energy matrices of electrodes to study ballistic electron transport properties in nanoscale systems. To reduce the high computational cost incurred in large systems, a…
Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue problems for differential operators on unbounded domains. In this paper we propose to detect and approximate the point spectra of such operators…
We consider the Generalized Trust Region Subproblem (GTRS) of minimizing a nonconvex quadratic objective over a nonconvex quadratic constraint. A lifting of this problem recasts the GTRS as minimizing a linear objective subject to two…
Nonlinear eigenvalue problems (NEPs) present significant challenges due to their inherent complexity and the limitations of traditional linear eigenvalue theory. This paper addresses these challenges by introducing a nonlinear…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
Under the hypothesis that the deviations of the desired eigenvectors of the matrix $A$ from the underlying subspace tend to zero, the Ritz vectors may not converge and have poor or little accuracy. This phenomenon is not unusual and…
A generalized eigenvalue algorithm for tridiagonal matrix pencils is presented. The algorithm appears as the time evolution equation of a nonautonomous discrete integrable system associated with a polynomial sequence which has some…
This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix in large dimensional situations. We generalize the contour-integral based method in Mestre (2008) and present a local moment…
Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and efficiency. The existing package Guptri is very elegant but may sometimes be time-demanding, even for small and…
This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient…
In this paper the author introduces a new domain decomposition method for the solution of discretised integral equation eigenvalue problems. The new domain decomposition method is motivated by the so-called automated multi-level…
The QR algorithm is one of the three phases in the process of computing the eigenvalues and the eigenvectors of a dense nonsymmetric matrix. This paper describes a task-based QR algorithm for reducing an upper Hessenberg matrix to real…
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…