Toeplitz Covariance Matrices and the von Neumann Relative Entropy
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Sample covariances based on time-series data fail to be Toeplitz. The purpose of the paper is to suggest the von Neumann relative-entropy as a distance measure for approximating a positive-definite sample covariance by one having the Toeplitz structure. This leads to a convex optimization problem whose solution retains the property of being positive-definite.
KeywordsApproximation Structured matrices Positivity von Neumann entropy
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- T. T. Georgiou, “Spectral analysis based on the state covariance: the maximum entropy spectrum and linear fractional parameterization,”IEEE Trans. on Automatic Controlto appear.Google Scholar
- T. T. Georgiou and A. Lindquist, “Kullback-Leibler approximation of spectral density functions,” preprint, May 2002.Google Scholar
- S. KullbackInformation Theory and Statistics2nd ed. New York: Dover Books, 1968 (1st ed. New York: John Wiley, 1959).Google Scholar