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Bounds on the extreme eigenvalues of positive-definite Toeplitz matrices

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1 Author(s)
A. Dembo ; Dept. of Electr. Eng., Technion, Israel Inst. of Technol., Haifa, Israel

Easily computable bounds on the extreme eigenvalues of positive semidefinite (PSD) Toeplitz matrices are presented. The bounds are especially suitable for matrices of relatively small dimension. The bounds are derived for the wider class of PSD Hermitian matrices and interpreted via the Levinson-Durbin Algorithm for Toeplitz matrices. As a by-product of this derivation an order-recursive algorithm for the eigenvector/eigenvalue decomposition is obtained, and certain properties of the eigenvalues distribution are revealed

Published in:

IEEE Transactions on Information Theory  (Volume:34 ,  Issue: 2 )