An efficient algorithm for a large Toeplitz set of linear equations

An algorithm is presented which requires
2n^{2} + 8n \log_{2} n - n
computations for solving a set of
n
linear Toeplitz equations for n = 2
^k
, where k is a positive integer. The previously known algorithms require a minimum of 3n
²
computations. The major advantage of the algorithm is realized for those applications where the set of n Toeplitz equations Tx = c is to be solved for a different c and the same T for the unknown x. Each additional solution requires storing only (4n + 1) elements from the first solution and
6n \log_{2} n + 3n
computations.