A fast algorithm for LR-2 factorization of Toeplitz matrices


Glentis, George-Othon (1995) A fast algorithm for LR-2 factorization of Toeplitz matrices. Signal processing, 42 (1). pp. 19-36. ISSN 0165-1684

open access
Abstract:In this paper a new order recursive algorithm for the efficient −1 factorization of Toeplitz matrices is described. The proposed algorithm can be seen as a fast modified Gram-Schmidt method which recursively computes the orthonormal columns i, i = 1,2, …,p, of , as well as the elements of R−1, of a Toeplitz matrix with dimensions L × p. The factor estimation requires 8Lp MADS (multiplications and divisions). Matrix −1 is subsequently estimated using 3p2 MADS. A faster algorithm, based on a mixed and −1 updating scheme, is also derived. It requires 7Lp + 3.5p2 MADS. The algorithm can be efficiently applied to batch least squares FIR filtering and system identification. When determination of the optimal filter is the desired task it can be utilized to compute the least squares filter in an order recursive way. The algorithm operates directly on the experimental data, overcoming the need for covariance estimates. An orthogonalized version of the proposed −1 algorithm is derived. Matlab code implementing the algorithm is also supplied.
Item Type:Article
Copyright:© 1995 Elsevier Science
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/15459
Official URL:https://doi.org/10.1016/0165-1684(94)00113-E
Export this item as:BibTeX
HTML Citation
Reference Manager


Repository Staff Only: item control page

Metis ID: 112338