Computing a Lower Bound of the Smallest Eigenvalue of a Symmetric Positive-Definite Toeplitz Matrix

In this correspondence, several algorithms to compute a lower bound of the smallest eigenvalue of a symmetric positive-definite Toeplitz matrix are described and compared in terms of accuracy and computational efficiency. Exploiting the Toeplitz structure of the considered matrix, new theoretical in...

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Veröffentlicht in:	IEEE transactions on information theory 2008-10, Vol.54 (10), p.4726-4731
Hauptverfasser:	Laudadio, T., Mastronardi, N., Van Barel, M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Accuracy Algorithms Applied sciences Cholesky factorization Computation Computational efficiency Computer networks Control system synthesis Councils Eigenvalues Eigenvalues and eigenfunctions Exact sciences and technology Information theory Information, signal and communications theory Iterative algorithms Levinson-Durbin algorithm Lower bounds Mathematics Matrix QR factorization Read-write memory Signal processing algorithms Sun Symmetric matrices symmetric positive-definite matrix Telecommunications and information theory Toeplitz matrix
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Beschreibung
Zusammenfassung:	In this correspondence, several algorithms to compute a lower bound of the smallest eigenvalue of a symmetric positive-definite Toeplitz matrix are described and compared in terms of accuracy and computational efficiency. Exploiting the Toeplitz structure of the considered matrix, new theoretical insights are derived and an efficient implementation of some of the aforementioned algorithms is provided.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2008.928966