8 papers
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…