An efficient algorithm for a large Toeplitz set of linear equations

An algorithm is presented which requires2n² + 8n log₂ n - ncomputations for solving a set ofnlinear Toeplitz equations for n = 2k, where k is a positive integer. The previously known algorithms require a minimum of 3n2computations. 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 and6n log₂ n + 3ncomputations.