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.

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