  We present a circulant and skew-circulant splitting (CSCS) iterative method
for solving large sparse continuous Sylvester equations $AX + XB = C$, where
the coefficient matrices $A$ and $B$ are Toeplitz matrices. A theoretical study
shows that if the circulant and skew-circulant splitting factors of $A$ and $B$
are positive semi-definite and at least one is positive definite (not
necessarily Hermitian), then the CSCS method converges to the unique solution
of the Sylvester equation. In addition, we obtain an upper bound for the
convergence factor of the CSCS iteration. This convergence factor depends only
on the eigenvalues of the circulant and skew-circulant splitting matrices. A
computational comparison with alternative methods reveals the efficiency and
reliability of the proposed method.
