O(nlog2n) determinant computation of a Toeplitz matrix and fast variance estimation Original Research Article

The determinant of an n × n Toeplitz matrix can be computed in O(n) flops given the associated generalised Shur constants, and these can be found from the fast algorithms of de Hoog and Ammar and Gragg without increasing the algorithmsʹ asymptotic complexity. An important consequence is an estimate of O(nlog2n) flops for computing variance parameters in certain multivariate normal models.