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.
Scopus Subject Areas
- Computational Mathematics
- Applied Mathematics
- Approximate inverse-free preconditioners
- Gohberg-Semencul formula
- Preconditioned conjugate gradient method
- Toeplitz matrices