51 citations · 136 across the 35 of their papers we have counts for
35 papers
Analysis of Block Jacobi/Gauss-Seidel and additive/multiplicative Schwarz preconditioning through the theory of GLT sequences, with applications to domain decomposition discretizations
Carlo Garoni, Abdessadek Rifqui, Stefano Serra-Capizzano
When a linear differential problem is discretized by a linear numerical method characterized by a mesh fineness parameter , the computation of the numerical solution reduces to…
Outlier-free isogeometric discretizations for Laplace eigenvalue problems: closed-form eigenvalue and eigenvector expressions
Noureddine Lamsahel, Carla Manni, Ahmed Ratnani +2
We derive explicit closed-form expressions for the eigenvalues and eigenvectors of the matrices resulting from isogeometric Galerkin discretizations based on outlier-free spline su…
A note on the convergence of multigrid methods for the Riesz-space equation and an application to image deblurring
Danyal Ahmad, Marco Donatelli, Mariarosa Mazza +2
In the past decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional diffe…
Spectral properties of flipped Toeplitz matrices
Giovanni Barbarino, Sven-Erik Ekström, Carlo Garoni +3
We study the spectral properties of flipped Toeplitz matrices of the form , where is the Toeplitz matrix generated by the function and $Y…
From asymptotic distribution and vague convergence to uniform convergence, with numerical applications
Giovanni Barbarino, Sven-Erik Ekström, Carlo Garoni +3
Let be a sequence of finite multisets of real numbers such that as , and let …
Modeling excitable cells with the EMI equations: spectral analysis and iterative solution strategy
Pietro Benedusi, Paola Ferrari, Marie Rognes +1
In this work, we are interested in solving large linear systems stemming from the Extra-Membrane-Intra (EMI) model, which is employed for simulating excitable tissues at a cellular…
A smoothing analysis for multigrid methods applied to tempered fractional problems
D. Ahmad, M. Donatelli, M. Mazza +2
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted…
Theoretical results for eigenvalues, singular values, and eigenvectors of (flipped) Toeplitz matrices and related computational proposals
Giovanni Barbarino, Sven-Erik Ekström, Stefano Serra-Capizzano +1
In a series of recent papers the spectral behavior of the matrix sequence is studied in the sense of the spectral distribution, where is the main antidiagonal…
Fast algebraic multigrid for block-structured dense and Toeplitz-like-plus-Cross systems arising from nonlocal diffusion problems
Minghua Chen, Rongjun Cao, Stefano Serra-Capizzano
Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation oper…
A note on the spectral analysis of matrix sequences via GLT momentary symbols: from all-at-once solution of parabolic problems to distributed fractional order matrices
Matthias Bolten, Sven-Erik Ekström, Isabella Furci +1
The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization with space-time grid for a…
Rectangular GLT Sequences
Giovanni Barbarino, Carlo Garoni, Mariarosa Mazza +1
The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of square matrices arising from the disc…
Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory
M. Bogoya, S. E. Ekström, S. Serra-Capizzano
Under appropriate technical assumptions, the simple-loop theory allows to deduce various types of asymptotic expansions for the eigenvalues of Toeplitz matrices generated by a func…
On the extreme eigenvalues and asymptotic conditioning of a class of Toeplitz matrix-sequences arising from fractional problems
M. Bogoya, S. M. Grudsky, M. Mazza +1
The analysis of the spectral features of a Toeplitz matrix-sequence , generated by a symbol , real-valued almost everywhe…
Asymptotic spectra of large (grid) graphs with a uniform local structure (part II): numerical applications
Andrea Adriani, Davide Bianchi, Paola Ferrari +1
In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain , . When $Ω…
Spectral and norm estimates for matrix sequences arising from a finite difference approximation of elliptic operators
Armando Coco, Sven-Erik Ekström, Giovanni Russo +2
When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the…
A matrix-theoretic spectral analysis of incompressible Navier-Stokes staggered DG approximation and related solvers
Mariarosa Mazza, Matteo Semplice, Stefano Serra-Capizzano +1
The incompressible Navier-Stokes equations are solved in a channel, using a Discontinuous Galerkin method over staggered grids. The resulting linear systems are studied both in ter…
Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix-sequences
Paola Ferrari, Isabella Furci, Stefano Serra-Capizzano
In recent years, motivated by computational purposes, the singular value and spectral features of the symmetrization of Toeplitz matrices generated by a Lebesgue integrable functio…
Toeplitz Momentary Symbols: definition, results, and limitations in the spectral analysis of Structured Matrices
Matthias Bolten, Sven-Erik Ekström, Isabella Furci +1
A powerful tool for analyzing and approximating the singular values and eigenvalues of structured matrices is the theory of GLT sequences. By the GLT theory one can derive a functi…
Asymptotic spectra of large (grid) graphs with a uniform local structure
Andrea Adriani, Davide Bianchi, Stefano Serra-Capizzano
We are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain , . We assume to be Lebesgu…
Multigrid methods for block-Toeplitz linear systems: convergence analysis and applications
Marco Donatelli, Paola Ferrari, Isabella Furci +2
In the past decades, multigrid methods for linear systems having multilevel Toeplitz coefficient matrices with scalar entries have been largely studied. On the other hand, only few…
A note on the spectral distribution of symmetrized Toeplitz sequences
Sean Hon, Mohammad Ayman Mursaleen, Stefano Serra-Capizzano
The singular value and spectral distribution of Toeplitz matrix sequences with Lebesgue integrable generating functions is well studied. Early results were provided in the classica…
A Multigrid method for nonlocal problems: non-diagonally dominant Toeplitz-plus-tridiagonal systems
Minghua Chen, Sven-Erik Ekström, Stefano Serra-Capizzano
The nonlocal problems have been used to model very different applied scientific phenomena, which involve the fractional Laplacian when one looks at the Lévy processes and stochasti…
Isogeometric analysis for 2D and 3D curl-div problems: Spectral symbols and fast iterative solvers
Mariarosa Mazza, Carla Manni, Ahmed Ratnani +2
Alfvén-like operators are of interest in magnetohydrodynamics, which is used in plasma physics to study the macroscopic behavior of plasma. Motivated by this important and complex…
Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman-Kac equation
Minghua Chen, Weihua Deng, Stefano Serra-Capizzano
In this paper we derive new uniform convergence estimates for the V-cycle MGM applied to symmetric positive definite Toeplitz block tridiagonal matrices, by also discussing few con…