Related papers: Inexact Shift-and-Invert Arnoldi for Toeplitz Matr…
We introduce an efficient stable algorithm for transforms associated with expansions in Hermite functions interpolated at Hermite polynomial roots. The Hermite transform matrix can be factorised into a diagonal component and an orthogonal…
The property of being shift invariant and being reflexive or transitive in the case of the space of (asymmetric) truncated Toeplitz operators, and the space of (asymmetric) dual truncated operators is investigated. Most of the results…
We observe a sample of $n$ independent $p$-dimensional Gaussian vectors with Toeplitz covariance matrix $ \Sigma = [\sigma_{|i-j|}]_{1 \leq i,j \leq p}$ and $\sigma_0=1$. We consider the problem of testing the hypothesis that $\Sigma$ is…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…
The computation of the exponential of a tridiagonal matrix and its applications have always been of interest. One application considered here is when the method of lines is used to solve the heat equation, where the equation is transformed…
The conversion of resolvent conditions into semigroup estimates is crucial in the stability analysis of hyperbolic partial differential equations. For two families of multiple Toeplitz operators, we relate the power bound with a resolvent…
This paper studies two structured approximation problems: (1) Recovering a corrupted low-rank Toeplitz matrix and (2) recovering the range of a Fourier matrix from a single observation. Both problems are computationally challenging because…
Solving inverse problems by dynamical variant of the BC-method is basically reduced to inverting the connecting operator $C^T$ of the dynamical system, for which the problem is stated. Realizing the method numerically, one needs to invert…
We introduce a novel algorithm for approximating the logarithm of the determinant of a symmetric positive definite (SPD) matrix. The algorithm is randomized and approximates the traces of a small number of matrix powers of a specially…
Toeplitz matrices arise naturally in harmonic analysis, operator theory, and numerical analysis. In this note we investigate Toeplitz matrices whose coefficients depend on the matrix size through a scaled kernel $a_k=f(k/n)$. We show that…
Solving the Toeplitz systems, which is to find the vector $x$ such that $T_nx = b$ given an $n\times n$ Toeplitz matrix $T_n$ and a vector $b$, has a variety of applications in mathematics and engineering. In this paper, we present a…
We present a new superfast algorithm for solving Toeplitz systems. This algorithm is based on a relation between the solution of such problems and syzygies of polynomials or moving lines. We show an explicit connection between the…
In this work we consider a class of delay eigenvalue problems that admit a spectrum similar to that of a Hamiltonian matrix, in the sense that the spectrum is symmetric with respect to both the real and imaginary axis. More precisely, we…
This article is about finding the limit set for banded Toeplitz matrices. Our main result is a new approach to approximate the limit set $\Lambda(b)$ where $b$ is the symbol of the banded Toeplitz matrix. The new approach is geometrical and…
This paper discusses the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence…
Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…
In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…
A Toeplitz operator $T_\varphi$, $\varphi \in L^\infty(\mathbb{T}^n)$, is a partial isometry if and only if there exist inner functions $\varphi_1, \varphi_2 \in H^\infty(\mathbb{D}^n)$ such that $\varphi_1$ and $\varphi_2$ depends on…
The approximation of $e^{tA}B$ where $A$ is a large sparse matrix and $B$ a rectangular matrix is the key ingredient in many scientific and engineering computations. A powerful tool to manage the matrix exponential function is to resort to…
In this article, we improve previous results on exponential stability for analytic and Gevrey perturbations of quasi-convex integrable Hamiltonian systems. In particular, this provides a sharper upper bound on the speed of Arnold diffusion…