The Even-Odd Split Levinson Algorithm for Toeplitz Systems

We derive an algorithm for real symmetric Toeplitz systems with an arbitrary right-hand side, which differs from both the Levinson and the so-called "split Levinson" algorithms. While exploiting ideas from the split Levinson approach, it also takes advantage of the even-odd properties of Toeplitz matrices. For a system of order n, our algorithm achieves a complexity of $\frac{5}{2}n^2 + {\cal O}(n)$ flops on a sequential machine, compared to $3n^2 + {\cal O}(n)$ flops for the split Levinson algorithm and $4n^2 + {\cal O}(n)$ flops for the classical Levinson algorithm.