50 citations · 99 across the 15 of their papers we have counts for
24 papers
Convergent spectral inclusion sets for banded matrices
Simon N. Chandler-Wilde, Ratchanikorn Chonchaiya, Marko Lindner
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion…
Half-line compressions and finite sections of discrete Schrödinger operators with integer-valued potentials
Marko Lindner, Riko Ukena
We study 1D discrete Schrödinger operators with integer-valued potential and show that, , invertibility (in fact, even just Fredholmness) of always implies invertibili…
Spectral approximation of generalized Schrödinger operators via approximation of subwords
Fabian Gabel, Dennis Gallaun, Julian Großmann +2
We demonstrate criteria, purely based on finite subwords of the potential, to guarantee spectral inclusion as well as Hausdorff approximation of pseudospectra or even spectra of ge…
A note on Hausdorff-convergence of pseudospectra
Marko Lindner, Dennis Schmeckpeper
For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in…
Minimal Families of Limit Operators
Marko Lindner
We study two abstract scenarios, where an operator family has a certain minimality property. In both scenarios, it is shown that norm, spectrum and resolvent are the same for all f…
Finite Sections of Periodic Schrödinger Operators
Fabian Gabel, Dennis Gallaun, Julian Großmann +2
We study discrete Schrödinger operators with periodic potentials as they are typically used to approximate aperiodic Schrödinger operators like the Fibonacci Hamiltonian. We pr…
Finite section method for aperiodic Schrödinger operators
Fabian Gabel, Dennis Gallaun, Julian Großmann +2
We consider 1D discrete Schrödinger operators with aperiodic potentials given by a Sturmian word, which is a natural generalisation of the Fibonacci Hamiltonian. Via a standard app…
Circulant matrices: norm, powers, and positivity
Marko Lindner
In their recent paper "The spectral norm of a Horadam circulant matrix", Merikoski, Haukkanen, Mattila and Tossavainen study under which conditions the spectral norm of a general r…
Finite sections of the Fibonacci Hamiltonian
Marko Lindner, Hagen Söding
We study finite but growing principal square submatrices of the one- or two-sided infinite Fibonacci Hamiltonian . Our results show that such a sequence , no matter…
Recycling Givens rotations for the efficient approximation of pseudospectra of band-dominated operators
Marko Lindner, Torge Schmidt
We study spectra and pseudospectra of certain bounded linear operators on . The operators are generally non-normal, and their matrix representation has a chara…
On the spectrum of operator families on discrete groups over minimal dynamical systems
Siegfried Beckus, Daniel Lenz, Marko Lindner +1
It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of…
Coburn's Lemma and the Finite Section Method for Random Jacobi Operators
Simon N. Chandler-Wilde, Marko Lindner
We study the spectra and pseudospectra of finite and infinite tridiagonal random matrices, in the case where each of the diagonals varies over a separate compact set, say $U,V,W\su…
Essential pseudospectra and essential norms of band-dominated operators
Raffael Hagger, Marko Lindner, Markus Seidel
An operator on an -space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. The coset of in th…
Note on spectra of non-selfadjoint operators over dynamical systems
Siegfried Beckus, Daniel Lenz, Marko Lindner +1
We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynami…
An Affirmative Answer to a Core Issue on Limit Operators
Marko Lindner, Markus Seidel
An operator on an -space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. It is known that a rich…
The Main Diagonal of a Permutation Matrix
Marko Lindner, Gilbert Strang
By counting 1's in the "right half" of consecutive rows, we locate the main diagonal of any doubly infinite permutation matrix with bandwidth . Then the matrix can be corre…
On the Spectra and Pseudospectra of a Class of Non-Self-Adjoint Random Matrices and Operators
Simon N. Chandler-Wilde, Ratchanikorn Chonchaiya, Marko Lindner
In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous…
Finite sections of random Jacobi operators
Marko Lindner, Steffen Roch
This article is about a problem in the numerical analysis of random operators. We study a version of the finite section method for the approximate solution of equations in i…
Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation
Timo Betcke, Simon N. Chandler-Wilde, Ivan G. Graham +2
We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have pro…
On the integer points in a lattice polytope: n-fold Minkowski sum and boundary
Marko Lindner, Steffen Roch
In this article we compare the set of integer points in the homothetic copy of a lattice polytope with the set of all sums with $x_1,...,x_n\…
Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices
Simon N. Chandler-Wilde, Marko Lindner
In the first half of this text we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch & Silbermann and…
Eigenvalue problem meets Sierpinski triangle: computing the spectrum of a non-self-adjoint random operator
Simon Chandler-Wilde, Ratchanikorn Chonchaiya, Marko Lindner
The purpose of this paper is to prove that the spectrum of the non-self-adjoint one-particle Hamiltonian proposed by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433--6443) has…
Two stable modifications of the finite section method
Marko Lindner
In this article we demonstrate and compare two modified versions of the classical finite section method for band-dominated operators in case the latter is not stable. For both meth…
Approximating the inverse of banded matrices by banded matrices with applications to probability and statistics
Peter J. Bickel, Marko Lindner
In the first part of this paper we give an elementary proof of the fact that if an infinite matrix , which is invertible as a bounded operator on , can be uniformly appr…