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Approximate inverse-free preconditioners for Toeplitz matrices |
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| Authors: | You-Wei Wen Wai-Ki ChingMichael Ng |
| Affiliation: | a Department of Mathematics, Kunming University of Science and Technology, PR China b Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong c Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong |
| Abstract: | 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. |
| Keywords: | Approximate inverse-free preconditioners Gohberg-Semencul formula Preconditioned conjugate gradient method Toeplitz matrices |
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