Marco Donatelli

A V -cycle Multigrid for multilevel matrix algebras: proof of optimality

We analyze the convergence rate of a multigrid method for multilevel linear systems whose coefficient matrices are generated by a real and nonnegative multivariate polynomial f and belong to multilevel matrix algebras like circulant, tau, Hartley, or are of Toeplitz type. In the case of matrix algebra linear systems, we prove that the convergence rate is independent of the system dimension even in presence of asymptotical ill-conditioning (this happens iff f takes the zero value). More precisely, if the d-level coefficient matrix has partial dimension nr at level r, with

Anti-reflective boundary conditions and re-blurring

{r=1, \ldots, d}

Spectral analysis and structure preserving preconditioners for fractional diffusion equations

, then the size of the system is

Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring ∗

{{N(\varvec{n})=\prod_{r=1}^d n_r}}

A multigrid for image deblurring with Tikhonov regularization

,