Geodesic
Solving linear systems with a Levinson-like solver
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 243-269
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},
     year = {2007},
     volume = {26},
     zbl = {1171.65366},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a12/}
}
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AU  - Mastronardi,  Nicola
AU  - Van Barel,  Marc
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EP  - 269
VL  - 26
UR  - http://geodesic.mathdoc.fr/item/ETNA_2007__26__a12/
LA  - en
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%0 Journal Article
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%A Mastronardi,  Nicola
%A Van Barel,  Marc
%T Solving linear systems with a Levinson-like solver
%J Electronic transactions on numerical analysis
%D 2007
%P 243-269
%V 26
%U http://geodesic.mathdoc.fr/item/ETNA_2007__26__a12/
%G en
%F ETNA_2007__26__a12
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/