Spectral analysis for preconditioning of multi-dimensional Riesz fractional diffusion equations

X Huang, XL Lin, MK Ng, HW Sun - arXiv preprint arXiv:2102.01371, 2021 - arxiv.org
In this paper, we analyze the spectra of the preconditioned matrices arising from discretized
multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is …

The GLT class as a generalized Fourier analysis and applications

S Serra-Capizzano - Linear Algebra and its Applications, 2006 - Elsevier
Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced
as a generalization both of classical Toeplitz sequences and of variable coefficient …

Symbol-based multigrid methods for Galerkin B-spline isogeometric analysis

M Donatelli, C Garoni, C Manni… - SIAM Journal on …, 2017 - SIAM
We consider the stiffness matrices arising from the Galerkin B-spline isogeometric analysis
discretization of classical elliptic problems. By exploiting their specific spectral properties …

V-cycle optimal convergence for certain (multilevel) structured linear systems

A Arico, M Donatelli, SS Capizzano - SIAM Journal on Matrix Analysis and …, 2004 - SIAM
In this paper we are interested in the solution by multigrid strategies of multilevel linear
systems whose coefficient matrices belong to the circulant, Hartley, or τ algebras or to the …

[HTML][HTML] Antireflective boundary conditions for deblurring problems

M Donatelli, S Serra-Capizzano - Journal of Electrical and …, 2010 - Wiley Online Library
This survey paper deals with the use of antireflective boundary conditions for deblurring
problems where the issues that we consider are the precision of the reconstruction when the …

Preconditioners for fractional diffusion equations based on the spectral symbol

N Barakitis, SE Ekström… - Numerical Linear Algebra …, 2022 - Wiley Online Library
It is well known that the discretization of fractional diffusion equations with fractional
derivatives α∈(1, 2) α ∈\left (1, 2\right), using the so‐called weighted and shifted Grünwald …

A matrix-theoretic spectral analysis of incompressible Navier–Stokes staggered DG approximations and a related spectrally based preconditioning approach

M Mazza, M Semplice, S Serra-Capizzano… - Numerische …, 2021 - Springer
Abstract The incompressible Navier–Stokes equations are solved in a channel, using a
Discontinuous Galerkin method over staggered grids. We study the structure and the …

[HTML][HTML] Fine spectral estimates with applications to the optimally fast solution of large FDE linear systems

M Bogoya, SM Grudsky, S Serra–Capizzano… - BIT Numerical …, 2022 - Springer
In the present article we consider a type of matrices stemming in the context of the numerical
approximation of distributed order fractional differential equations (FDEs). From one side …

[HTML][HTML] Essential spectral equivalence via multiple step preconditioning and applications to ill conditioned Toeplitz matrices

D Noutsos, S Serra-Capizzano, P Vassalos - Linear Algebra and its …, 2016 - Elsevier
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 …

Multigrid methods for Toeplitz linear systems with different size reduction

M Donatelli, S Serra-Capizzano, D Sesana - BIT Numerical Mathematics, 2012 - Springer
Starting from the spectral analysis of g-circulant matrices, we study the convergence of a
multigrid method for circulant and Toeplitz matrices with various size reductions. We assume …