Geodesic
Solving linear systems with a Levinson-like solver
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 243-269.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we will present a general framework for solving linear systems of equations. The solver is based on the Levinson-idea for solving Toeplitz systems of equations. We will consider a general class of matrices, defined as the class of simple -Levinson conform matrices. This class incorporates, for instance, $\sterling $#############$\ddot $§$\copyright $### semiseparable, band, companion, arrowhead and many other matrices. For this class, we will derive a solver of complexity . The system solver is written inductively, and uses in every step , the solution of a so-called $\sterling $#########$$ ! th order Yule-Walker-like equation. The algorithm obtained first has complexity . Based, however $$###$ ! \sterling $######## on the specific structure of the simple -Levinson conform matrices, we will be able to further reduce the $\sterling $########$\ddot $§$\copyright $###$$"# complexity of the presented method, and get an order algorithm.$$
Classification : 65F05
Keywords: levinson, yule-Walker, look-ahead, system solving, levinson conform matrices 
@article{ETNA_2007__26__a12,
     author = {Vandebril, Raf and Mastronardi, Nicola and Van Barel, Marc},
     title = {Solving linear systems with a {Levinson-like} solver},
     journal = {Electronic transactions on numerical analysis},
     pages = {243--269},
     publisher = {mathdoc},
     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a12/}
}
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Vandebril, Raf; Mastronardi, Nicola; Van Barel, Marc. Solving linear systems with a Levinson-like solver. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 243-269. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a12/