9 papers · 1 filter
Matrix algebras with orthogonal Cauchy-like transforms and Toeplitz approximation: a negative result
Dario Fasino, Davide Furchì, Valerio Loi +1
We consider newly designed matrix algebras associated with Cauchy orthogonal transforms. In this work, we are interested in checking the approximation of Toeplitz matrices using al…
Lagrange interpolation processes based on the zeros of anti-Gauss Jacobi polynomials
Patricia Díaz de Alba, Luisa Fermo, Valerio Loi +1
This paper introduces and investigates a new Lagrange interpolation process based on the zeros of anti-Gauss Jacobi polynomials. Fundamental properties of anti-Gauss nodes, includi…
Anti-Gauss Lagrange interpolation: Christoffel-Darboux form, barycentric representation, and orthogonal expansion
Patricia Díaz de Alba, Luisa Fermo, Valerio Loi
The paper deals with new formulations of a Lagrange interpolant polynomial based on the nodes of the well-known anti-Gauss rule. A first representation is given in terms of the cla…
Weyl distributions, spectral properties, and circulant approximation results for quaternion block multilevel Toeplitz matrix sequences
Ayoub Lailoune, Valerio Loi, Stefano Serra-Capizzano
The present work contains a comprehensive treatment of Weyl eigenvalue and singular value distributions, \val{Schatten -norm estimates, spectral localization and positive-defini…
Spectral analysis of the stiffness matrix sequence in the approximated Stokes equation
Samuele Ferri, Chiara Giraudo, Valerio Loi +2
In the present paper, we analyze in detail the spectral features of the matrix sequences arising from the Taylor-Hood - approximation of variable viscos…
Geometric means of HPD GLT matrix-sequences: a maximal result beyond invertibility assumptions on the GLT symbols
Asiim Ilyas, Muhammad Faisal Khan, Valerio Loi +1
In the current work, we consider the study of the spectral distribution of the geometric mean matrix-sequence of two matrix-sequences formed by Hermitian Positi…
Blocking structures, approximation, and preconditioning
Nikos Barakitis, Marco Donatelli, Samuele Ferri +3
We consider block-structured matrices , where the blocks are of (block) unilevel Toeplitz type with matrix-valued generating functions. Under mild assumptions on t…
Approximation of the Hilbert Transform on the unit circle
Luisa Fermo, Valerio Loi
The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegö and anti-Szegö quadrature formulas. These schemes exhibit maximum precision…
A note on eigenvalues and singular values of variable Toeplitz matrices and matrix-sequences, with application to variable two-step BDF approximations to parabolic equations
Nikos Barakitis, Valerio Loi, Stefano Serra-Capizzano
Here, we consider a more general class of matrix-sequences and we prove that they belong to the maximal -algebra of generalized locally Toeplitz (GLT) matrix-sequences. Then, we…