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

  • Authors:

  • G. N. Newsam;C. R. Dietrich

  • Affiliations:

  • Inf. Technol. Div., Defence Sci. & Technol. Organ., Salisbury, SA;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

Dembo et al. (see ibid., vol. 35, pp. 1206-1212, 1989) showed that an N×N positive definite Toeplitz matrix T could be embedded in a 2M×2M nonnegative definite circulant matrix S with M=O[κ(T)N 2]. This paper shows that the size of the embedding can be reduced to M=O[κ(T)1/2N5/4] and that this is best possible for the technique presented by Dembo et al