Circulant and skew-circulant splitting methods for Toeplitz systems

We study efficient iterative methods for Toeplitz systems based on the circulant and skew-circulant splitting (CSCS) of the Toeplitz matrix. Theoretical analysis show that if the circulant and the skew-circulant splitting matrices are positive definite, then the CSCS method converges to the unique solution of the system of linear equations. Moreover, we derive an upper bound of the contraction factor of the CSCS iteration which is dependent solely on the spectra of the circulant and the skew-circulant matrices involved. Numerical examples are presented to demonstrate the method.