Recursive eigendecomposition via autoregressive analysis and ago-antagonistic regularization

Author

Barbaresco, Frèdèric

Author_Institution

Radar Dev./Algorithms & New Concepts Dept., Thomson-CSF, Bagneux, France

Volume

5

fYear

1997

fDate

21-24 Apr 1997

Firstpage

3969

Abstract

A new recursive eigendecomposition algorithm of complex Hermitian Toeplitz matrices is studied. Based on Trench´s inversion of Toeplitz matrices from their autoregressive analysis, we have developed a fast recursive iterative algorithm that takes into account the rank-one modification of successive order Toeplitz matrices. To speed up the computational time and to increase numerical stability of ill-conditioned eigendecomposition in case of very short data records analysis, we have extended this method by introducing an ago-antagonistic regularized reflection coefficient via Levinson equation. We provide a geometrical interpretation of this new recursive eigendecomposition

Keywords

Hermitian matrices; Toeplitz matrices; autoregressive processes; computational complexity; eigenvalues and eigenfunctions; iterative methods; matrix decomposition; matrix inversion; numerical stability; spectral analysis; Levinson equation; Trench´s inversion; agoantagonistic regularization; autoregressive analysis; complex Hermitian Toeplitz matrices; computational time; fast recursive iterative algorithm; geometrical interpretation; numerical stability; rank-one modification; recursive eigendecomposition algorithm; reflection coefficient; short data records analysis; spectral analysis; successive order Toeplitz matrice; time-Doppler spectrum; Algorithm design and analysis; Data analysis; Eigenvalues and eigenfunctions; Equations; Iterative algorithms; Numerical stability; Radar; Reflection; Robustness; Virtual reality;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on

Conference_Location

Munich

ISSN

1520-6149

Print_ISBN

0-8186-7919-0

Type

conf

DOI

10.1109/ICASSP.1997.604794

Filename

604794