Bounds on the size of nonnegative definite circulant embeddings of positive definite Toeplitz matrices

Dembo et al. (see ibid., vol. 35, pp. 1206-1212, 1989) showed that an N/spl times/N positive definite Toeplitz matrix T could be embedded in a 2M/spl times/2M nonnegative definite circulant matrix S with M=O[/spl kappa/(T)N/sup 2/]. This paper shows that the size of the embedding can be reduced to M=O[/spl kappa/(T)/sup 1/2/N/sup 5/4/] and that this is best possible for the technique presented by Dembo et al.<
>