Time-variant displacement structure and triangular arrays

Author

Sayed, Ali H. ; Lev-Ari, Hanoch ; Kailath, Thomas

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

42

Issue

5

fYear

1994

fDate

5/1/1994 12:00:00 AM

Firstpage

1052

Lastpage

1062

Abstract

The authors extend the concept of displacement structure to time-variant matrices and use it to efficiently and recursively propagate the Cholesky factor of such matrices. A natural implementation of the algorithm is via a modular triangular array of processing elements. When the algorithm is applied to solve the normal equations that arise in adaptive least-squares filtering, they get the so-called QR algorithm, with the extra bonus of a parallelizable procedure for determining the weight vector. It is shown that the general algorithm can also be implemented in time-variant lattice form; a specialization of this result yields a time-variant Schur algorithm

Keywords

filtering and prediction theory; least squares approximations; matrix algebra; time-varying systems; Cholesky factor; QR algorithm; adaptive least-squares filtering; algorithm; processing elements; time-variant Schur algorithm; time-variant displacement structure; time-variant lattice; time-variant matrices; triangular arrays; weight vector; Adaptive filters; Contracts; Equations; Filtering algorithms; Helium; History; Information systems; Lattices; Mathematics; Signal processing algorithms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.295212

Filename

295212