A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time–space fractional diffusion equation.

A block lower triangular Toeplitz system arising from the time–space fractional diffusion equation is discussed. For efficient solutions of such the linear system, the preconditioned biconjugate gradient stabilized method and the flexible general minimal residual method are exploited. The main contribution of this paper has two aspects: (i) A block bi-diagonal Toeplitz preconditioner is developed for the block lower triangular Toeplitz system, whose storage is of O (N) with N being the spatial grid number; (ii) A new skew-circulant preconditioner is designed to accelerate the inverse of the block bi-diagonal Toeplitz preconditioner multiplying a vector. Numerical experiments are given to demonstrate the effectiveness of our two proposed preconditioners. • The block lower triangular Toeplitz system arising from time–space fractional diffusion equation is discussed. • A limited-memory block bi-diagonal Toeplitz (B2T) preconditioner is developed for the system. • A new skew-circulant preconditioner is designed to compute the inverse of the B2T preconditioner multiplying a vector. • Numerical examples are given to demonstrate the efficiency of our preconditioning strategy. [ABSTRACT FROM AUTHOR]