Department of Mathematics
Approximate inverse-free preconditioners for Toeplitz matrices
In this paper, we propose approximate inverse-free preconditioners for solving Toeplitz systems. The preconditioners are constructed based on the famous Gohberg-Semencul formula. We show that if a Toeplitz matrix is generated by a positive bounded function and its entries enjoys the off-diagonal decay property, then the eigenvalues of the preconditioned matrix are clustered around one. Experimental results show that the proposed preconditioners are superior to other existing preconditioners in the literature. © 2011 Elsevier Inc. All rights reserved.
Approximate inverse-free preconditioners, Gohberg-Semencul formula, Preconditioned conjugate gradient method, Toeplitz matrices
Source Publication Title
Applied Mathematics and Computation
Wen, You-Wei, Wai-Ki Ching, and Michael Ng. "Approximate inverse-free preconditioners for Toeplitz matrices." Applied Mathematics and Computation 217.16 (2011): 6856-6867.