Search arXivSearch

arXiv · 2604.03823

A note on the spectral distribution of non-Hermitian block matrices with Toeplitz blocks

Abstract

In the present paper, we are concerned with the study of the spectral distribution of matrix-sequences showing a non-Hermitian block structure with Toeplitz blocks. We use the notion of geometric mean of matrices and the theory of Generalized Locally Toeplitz (GLT) sequences to perform our analysis and produce some numerical tests and visualizations to confirm our theoretical derivations.

Explore related subjects

Keep this discovery

BibTeXRIS

Andrea Adriani, Giacomo Tento. 2026-09-02. A note on the spectral distribution of non-Hermitian block matrices with Toeplitz blocks. https://arxiv.org/abs/2604.03823

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

Numerical experiments on the Hardy conjecture for the Gauss circle problem

The classical unsolved Gauss circle problem concerns estimating the error between the number of lattice points inside a circle and the area of the circle as its radius tends to infinity. About a century ago, Hardy proposed a conjecture concerning this problem. In this paper, we attempt to provide numerical evidence in support of the Hardy conjecture through large-scale numerical computations.

math.NT

Advancements in Spectral Collocation Methods for High-Order Eigenvalue Problems

This paper focuses on computing spectral solutions for high-order eigenvalue problems using an efficient discretization method based on Chebfun spectral discretization algorithms and domain truncation. We solve several numerical eigenvalue problems, demonstrating both the accuracy and computational efficiency of the proposed approach.

math.NA

$L^p$-Convergence Rate of Backward Euler Schemes for Monotone SDEs

We give a unified method to derive the strong convergence rate of the backward Euler scheme for monotone SDEs in $L^p(Ω)$-norm, with general $p \ge 4$. The results are applied to the backward Euler scheme of SODEs with polynomial growth coefficients. We also generalize the argument to the Galerkin-based backward Euler scheme of SPDEs with polynomial growth coefficients driven by multiplicative trace-class noise.

math.NA