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Simple bounds on the extreme eigenvalues of Toeplitz matrices

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1 Author(s)
Hertz, D. ; Rafael, Haifa, Israel

Simple bounds are presented on the extreme eigenvalues of n ×n-dimensional Hermitian Toeplitz matrices. Such a matrix, say Tn, is determined by its first row. The proposed bounds have low complexity O(n); furthermore, examples are presented for which the proposed bounds are tighter than the Slepian-Landau bounds at their best, i.e. when the extreme eigenvalues of the submatrix obtained by deleting the first row and first column of Tn are known exactly. The bounds are first presented on the extreme eigenvalues of Hermitian Toeplitz matrices: the corresponding bounds for real symmetric Toeplitz matrices follow as a special case. Then, these bounds are extended to Hermitian Toeplitz interval matrices

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Information Theory, IEEE Transactions on  (Volume:38 ,  Issue: 1 )