Related papers: Exact eigenvalue assignment of linear scalar syste…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
In this paper we solve the eigenvalue problem of stochastic Hamiltonian system with boundary conditions. Firstly, we extend the results in S. Peng \cite{peng} from time-invariant case to time-dependent case, proving the existence of a…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the…
This paper presents and implements an iterative feedback design algorithm for stabilisation of discrete-time switched systems under arbitrary switching regimes. The algorithm seeks state feedback gains so that the closed-loop switching…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
In this paper, using the linearization technique we write the Helmholtz transmission eigenvalue problem as an equivalent nonselfadjoint linear eigenvalue problem whose left-hand side term is a selfadjoint, continuous and coercive…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
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…
We calculate eigenvalues of one-dimensional quantum-systems by the exact numerical solution of the Lippmann-Schwinger equation, analogous to the scattering problem. To illustrate our method, we treat elementary problems: the harmonic and…
This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…
We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system…
In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…
The present paper introduces the analysis of the eigenvalue problem for the elasticity equations when the so called Navier-Lam\'e system is considered. Such a system introduces the displacement, rotation and pressure of some linear and…
The exact pole placement problem concerns computing a feedback gain that will assign the poles of a system, controlled via static state feedback, at a set of pre-specified locations. This is a classic problem in feedback control and…
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…
The pole assignment problem for descriptor systems is a classical inverse algebraic eigenvalue problem, which has attracted attention for decades. In this paper, we propose a direct method to solve the problem with the application of the…
In Density Functional Theory simulations based on the LAPW method, each self-consistent field cycle comprises dozens of large dense generalized eigenproblems. In contrast to real-space methods, eigenpairs solving for problems at distinct…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…