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It is known that every Toeplitz matrix 
$T$ enjoys a circulant and skew circulant splitting (denoted 
$\text{CSCS}$) i.e., 
$T=C-S$ a circulant matrix and 
$S$ a skew circulant matrix. Based on the variant of such a splitting (also referred to as $\text{CSCS}$), we first develop classical $\text{CSCS}$ iterative methods and then introduce shifted $\text{CSCS}$ iterative methods for solving hermitian positive definite Toeplitz systems in this paper. The convergence of each method is analyzed. Numerical experiments show that the classical $\text{CSCS}$ iterative methods work slightly better than the Gauss–Seidel 
$(\text{GS})$ iterative methods if the $\text{CSCS}$ is convergent, and that there is always a constant 
$\alpha $ such that the shifted $\text{CSCS}$ iteration converges much faster than the Gauss–Seidel iteration, no matter whether the $\text{CSCS}$ itself is convergent or not.
