Title :
Bounds on the extreme eigenvalues of positive-definite Toeplitz matrices
Author_Institution :
Dept. of Electr. Eng., Technion, Israel Inst. of Technol., Haifa, Israel
fDate :
3/1/1988 12:00:00 AM
Abstract :
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
Keywords :
eigenvalues and eigenfunctions; matrix algebra; Hermitian matrices; Levinson-Durbin Algorithm; bounds; eigenvector/eigenvalue decomposition; extreme eigenvalues; order-recursive algorithm; positive-definite Toeplitz matrices; Amplitude modulation; Artificial intelligence; Eigenvalues and eigenfunctions; Linear discriminant analysis; Matrix decomposition; Sequential analysis; Symmetric matrices; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on
