Title :
Bounds on the size of nonnegative definite circulant embeddings of positive definite Toeplitz matrices
Author :
Newsam, G.N. ; Dietrich, C.R.
Author_Institution :
Inf. Technol. Div., Defence Sci. & Technol. Organ., Salisbury, SA, Australia
fDate :
7/1/1994 12:00:00 AM
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
Keywords :
information theory; matrix algebra; simulation; statistics; embedding size bounds; nonnegative definite circulant embeddings; positive definite Toeplitz matrices; statistical simulations; Australia; Covariance matrix; Density functional theory; Eigenvalues and eigenfunctions; Information geometry; Information theory; Maximum likelihood estimation; Probability distribution; Statistical distributions; Symmetric matrices;
Journal_Title :
Information Theory, IEEE Transactions on
