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-Sememcul formula. We show that if a Toepltiz 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.

• Type: Journal
• Year: 2011
• Where: AMC
• Authors: You-Wei Wen, Wai-Ki Ching, Michael Ng
• Keywords: AMC 2011, Approximate Inverse-free Preconditioners, Famous Gohberg-sememcul Formula, Modeling And Simulation, Positive Bounded Function