10 papers · 1 filter
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…
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,…