Lopsided scaled HSS preconditioner for steady-state space-fractional diffusion equations

For the discrete linear system resulting from certain steady-state space-fractional diffusion equations, we construct a lopsided scaled HSS (LSHSS) iteration method and establish its convergence theory. From the LSHSS, we obtain the corresponding matrix splitting preconditioner. By further replacing the involved Toeplitz matrix with certain circulant matrix, we construct a fast LSHSS (FLSHSS) preconditioner in order to accelerate the convergence rates of the Krylov subspace iteration methods. Theoretical analyses and numerical experiments show good performance of the FLSHSS preconditioning.