Related papers: Exact eigenvalue assignment of linear scalar syste…

We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral…

Given two real symmetric matrices, their eigenvalue configuration is the relative arrangement of their eigenvalues on the real line. In this paper, we consider the following problem: given two parametric real symmetric matrices and an…

In this paper, an original result in terms of a sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system…

A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to computing structured pseudospectra and their extremal points, and…

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…

Subspace methods are commonly used for finding approximate eigenvalues and singular values of large-scale matrices. Once a subspace is found, the Rayleigh-Ritz method (for symmetric eigenvalue problems) and Petrov-Galerkin projection (for…

We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method is used to approximate isolated eigenvalues. It is shown that entries…

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…

Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…

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…

Finding the eigenvalues connected to the covariance operator of a centred Hilbert-space valued Gaussian process is genuinely considered a hard problem in several mathematical disciplines. In statistics this problem arises for instance in…

We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schroedinger…

We propose a method to efficiently estimate the eigenvalues of any arbitrary (potentially weighted and/or directed) network of interacting dynamical agents from dynamical observations. These observations are discrete, temporal measurements…

Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed can enable new studies of fundamental science as well as more potential applications. In this work we discuss solving a system of…

We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions…

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…

The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…

We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit…

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…