69 citations · 163 across the 25 of their papers we have counts for
28 papers
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…
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…
Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method
Davide Bianchi, Marco Donatelli, Davide Furchì +1
The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decompositio…
Symmetrization Techniques in Image Deblurring
Marco Donatelli, Paola Ferrari, Silvia Gazzola
This paper presents a couple of preconditioning techniques that can be used to enhance the performance of iterative regularization methods applied to image deblurring problems with…
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…
Multigrid for two-sided fractional differential equations discretized by finite volume elements on graded meshes
Marco Donatelli, Rolf Krause, Mariarosa Mazza +1
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due t…
Symbol based convergence analysis in multigrid methods for saddle point problems
Matthias Bolten, Marco Donatelli, Paola Ferrari +1
Saddle point problems arise in a variety of applications, e.g., when solving the Stokes equations. They can be formulated such that the system matrix is symmetric, but indefinite,…
On the matrices in B-spline collocation methods for Riesz fractional equations and their spectral properties
Mariarosa Mazza, Marco Donatelli, Carla Manni +1
In this work, we focus on a fractional differential equation in Riesz form discretized by a polynomial B-spline collocation method. For an arbitrary polynomial degree , we show…
Graph approximation and generalized Tikhonov regularization for signal deblurring
Davide Bianchi, Marco Donatelli
Given a compact linear operator $\K$, the (pseudo) inverse $\K^\dagger$ is usually substituted by a family of regularizing operators which depends on $\K$ itself. Naturally,…
Graph Laplacian for image deblurring
Davide Bianchi, Alessandro Buccini, Marco Donatelli +1
Image deblurring is relevant in many fields of science and engineering. To solve this problem, many different approaches have been proposed and among the various methods, variation…
A symbol based analysis for multigrid methods for Block-Circulant and Block-Toeplitz Systems
Matthias Bolten, Marco Donatelli, Paola Ferrari +1
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 conve…
Compatibility, embedding and regularization of non-local random walks on graphs
Davide Bianchi, Marco Donatelli, Fabio Durastante +1
Several variants of the graph Laplacian have been introduced to model non-local diffusion processes, which allow a random walker to {\textquotedblleft jump\textquotedblright} to no…
An inexact non stationary Tikhonov procedure for large-scale nonlinear ill-posed problems
Stefania Bellavia, Marco Donatelli, Elisa Riccietti
In this work we consider the stable numerical solution of large-scale ill-posed nonlinear least squares problems with nonzero residual. We propose a non-stationary Tikhonov method…
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…
Anisotropic, interpolatory subdivision and multigrid
Maria Charina, Marco Donatelli, Lucia Romani +1
In this paper, we present a family of multivariate grid transfer operators appropriate for anisotropic multigrid methods. Our grid transfer operators are derived from a new family…
Convergence and normal continuity analysis of non-stationary subdivision schemes near extraordinary vertices and faces
Costanza Conti, Marco Donatelli, Lucia Romani +1
Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue.…
Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations
Hamid Moghaderi, Mehdi Dehghan, Marco Donatelli +1
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and comp…
Multigrid methods: grid transfer operators and subdivision schemes
Maria Charina, Marco Donatelli, Lucia Romani +1
The convergence rate of a multigrid method depends on the properties of the smoother and the so-called grid transfer operator. In this paper we define and analyze new grid transfer…
Regularization preconditioners for frame-based image deblurring with reduced boundary artifacts
Yuantao Cai, Marco Donatelli, Davide Bianchi +1
Thresholding iterative methods are recently successfully applied to image deblurring problems. In this paper, we investigate the modified linearized Bregman algorithm (MLBA) used i…
Iterated fractional Tikhonov regularization
Davide Bianchi, Alessandro Buccini, Marco Donatelli +1
Fractional Tikhonov regularization methods have been recently proposed to reduce the oversmoothing property of the Tikhonov regularization in standard form, in order to preserve th…
Optimal order conditions for filter based regularization methods, with applications to variants of the Tikhonov method
Davide Bianchi, Marco Donatelli, Stefano Serra-Capizzano
We study filter based regularization methods for linear ill-posed problems between Hilbert spaces. We derive optimal order conditions under a-priori choice rules for the regulariza…
Spectral behavior of preconditioned non-Hermitian multilevel block Toeplitz matrices with matrix-valued symbol
Marco Donatelli, Carlo Garoni, Mariarosa Mazza +2
This note is devoted to preconditioning strategies for non-Hermitian multilevel block Toeplitz linear systems associated with a multivariate Lebesgue integrable matrix-valued symbo…
A Fast Alternating Minimization Algorithm for Total Variation Deblurring Without Boundary Artifacts
Zheng-Jian Bai, Daniele Cassani, Marco Donatelli +1
Recently, a fast alternating minimization algorithm for total variation image deblurring (FTVd) has been presented by Wang, Yang, Yin, and Zhang [{\em SIAM J. Imaging Sci.}, 1 (200…
Optimal preconditioning for image deblurring with Anti-Reflective boundary conditions
Pietro Dell'Acqua, Stefano Serra-Capizzano, Cristina Tablino Possio
Inspired by the theoretical results on optimal preconditioning stated by Ng, R.Chan, and Tang in the framework of Reflective boundary conditions (BCs), in this paper we present ana…