A symmetric algorithm for Toeplitz systems Original Research Article

We derive an algorithm for real symmetric Toeplitz systems with an arbitrary right-hand side. It differs from the Levinson algorithm in that the solution is built up from its middle component(s) outwards, rather than from top to bottom. We then exploit the symmetry of this method by solving separately for the even and odd parts of the right-hand side of the system. On a sequential machine, the complexity of our algorithm for a system of order n is image flops, compared to 4n2+O(n) flops for Levinsonʹs algorithm. The algorithm can be extended to nonsymmetric systems, just like Levinsonʹs algorithm.