Recursive eigendecomposition via autoregressive analysis and ago-antagonistic regularization

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.