Bounds on the size of nonnegative definite circulant embeddings of positive definite Toeplitz matrices
- 1 July 1994
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 40 (4) , 1218-1220
- https://doi.org/10.1109/18.335952
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 alKeywords
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