Preconditioning Toeplitz-plus-diagonal linear systems using the Sherman–Morrison–Woodbury formula

In order to solve the Toeplitz-plus-diagonal linear systems arising from image restorations efficiently, we propose a sparse approximate inverse preconditioner based on the Sherman–Morrison–Woodbury formula. The preconditioner can be constructed through an incomplete factorization combined with some dropping strategies. When the preconditioner is applied to the conjugate gradient method for solving the Toeplitz-plus-diagonal linear systems, numerical results show that our preconditioning method is more effective than other existing ones.