  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 differential equations (FDEs). In the current
work, we focus on multigrid methods for a Riesz-space FDE whose theoretical
convergence analysis of such multigrids is currently limited to the two-grid
method. Here we provide a detailed theoretical convergence study in the case of
V-cycle and W-cycle. Moreover, we discuss its use combined with a band
approximation and we compare the result with both $\tau$ and circulant
preconditionings. The numerical tests include 2D problems as well as the
extension to the case of a Riesz-FDE with variable coefficients. Finally, we
apply the best-performing method to an image deblurring problem with Tikhonov
regularization.
