Related papers: Pseudospectra of Loewner Matrix Pencils
We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity $\varepsilon$, permeability $\mu$ and conductivity $\sigma$, on finitely connected unbounded domains. The main result is…
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of…
This paper is concerned with the spectral properties of matrices associated with linear filters for the estimation of the underlying trend of a time series. The interest lies in the fact that the eigenvectors can be interpreted as the…
We present new examples of superintegrable matrix/eigenvalue models. These examples arise as a result of the exploration of the relationship between the theory of superintegrability and multivariate orthogonal polynomials. The new…
This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…
A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
Understanding how deep learning models represent data is currently difficult due to the limited number of methodologies available. This paper demonstrates a versatile and novel visualisation tool for determining the axis alignment of…
The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim,…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
In this paper, we consider the operator properties of various phononic eigenvalue problems. We aim to answer some fundamental questions about the eigenvalues and eigenvectors of phononic operators. These include questions about the…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix…
A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix $(\bb L^+)$ of a simple, undirected graph is proposed. % The nature of the underlying sub-problems is studied in detail…
In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well…
Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(\Delta)=\{\Delta_\l\}$ passing through the operator $\Delta$ such that…
The pseudospectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. In fact, for non-selfadjoint operators the resolvent could be very large outside the spectrum, making the…
We identify a class of operator pencils, arising in a number of applications, which have only real eigenvalues. In the one-dimensional case we prove a novel version of the Sturm oscillation theorem: if the dependence on the eigenvalue…
The estimation of cosmological constraints from observations of the large scale structure of the Universe, such as the power spectrum or the correlation function, requires the knowledge of the inverse of the associated covariance matrix,…
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…