Related papers: Blocking structures, approximation, and preconditi…
In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory…
This note is devoted to preconditioning strategies for non-Hermitian multilevel block Toeplitz linear systems associated with a multivariate Lebesgue integrable matrix-valued symbol. In particular, we consider special preconditioned…
In the literature, there exist several studies on symbol-based multigrid methods for the solution of linear systems having structured coefficient matrices. In particular, the convergence analysis for such methods has been obtained in an…
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…
We study the spectrum of an asymmetric random matrix with block structured variances. The rows and columns of the random square matrix are divided into $D$ partitions with arbitrary size (linear in $N$). The parameters of the model are the…
In recent years, there has been a renewed interest in preconditioning for multilevel Toeplitz systems, a research field that has been extensively explored over the past several decades. This work introduces novel preconditioning strategies…
In this paper we show that it is possible to retrieve structural information about complex block-oriented nonlinear systems, starting from linear approximations of the nonlinear system around different setpoints.The key idea is to monitor…
In this article we study the structured distance to singularity for a nonsingular matrix $A\in\mathbb{C}^{n\times n}$, with a prescribed linear structure $\mathcal{S}$ (for instance, a sparsity pattern, or a real Toeplitz structure), i.e.,…
We study a preconditioner for a Hermitian positive definite linear system, which is obtained as the solution of a matrix nearness problem based on the Bregman log determinant divergence. The preconditioner is of the form of a Hermitian…
Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…
The complex-shifted Laplacian systems arising in a wide range of applications. In this work, we propose an absolute-value based preconditioner for solving the complex-shifted Laplacian system. In our approach, the complex-shifted Laplacian…
In this note, we study the fast solution of Toeplitz linear systems with coefficient matrix $T_n(f)$, where the generating function $f$ is nonnegative and has a unique zero at zero of any real positive order $\theta$. As preconditioner we…
We study two specific symmetric random block Toeplitz (of dimension $k \times k$) matrices: where the blocks (of size $n \times n$) are (i) matrices with i.i.d. entries, and (ii) asymmetric Toeplitz matrices. Under suitable assumptions on…
In this paper, we describe and analyze the spectral properties of a symmetric positive definite inexact block preconditioner for a class of symmetric, double saddle-point linear systems. We develop a spectral analysis of the preconditioned…
We derive new perturbation bounds for eigenvalues of Hermitian matrices with block structures. The structures we consider range from a standard 2-by-2 block form to block tridiagonal and tridigaonal forms. The main idea is the observation…
The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…
Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…
In recent years there has been a growing attention on distribution results in the sense of Weyl for the collective behavior of eigenvalues and singular values of matrix-sequences. Starting from the work of Szeg\"o regarding the case of…
It is well known that if a matrix $A\in\mathbb C^{n\times n}$ solves the matrix equation $f(A,A^H)=0$, where $f(x, y)$ is a linear bivariate polynomial, then $A$ is normal; $A$ and $A^H$ can be simultaneously reduced in a finite number of…
Given a Lebesgue integrable function $f$ over $[0,2\pi]$, we consider the sequence of matrices $\{Y_nT_n[f]\}_n$, where $T_n[f]$ is the $n$-by-$n$ Toeplitz matrix generated by $f$ and $Y_n$ is the flip permutation matrix, also called the…