http://www.cnr.it/ontology/cnr/individuo/prodotto/ID8065
Solving linear systems with a Levinson-like solver (Articolo in rivista)
- Type
- Label
- Solving linear systems with a Levinson-like solver (Articolo in rivista) (literal)
- Anno
- 2007-01-01T00:00:00+01:00 (literal)
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- Vandebril R., Mastronardi N., Van Barel M. (literal)
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- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
- Rivista
- Note
- ISI Web of Science (WOS) (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- K.U.Leuven, Dept. Computerwetenschappen, Celestijnenlaan 200A, 3000 Leuven (Heverlee), Belgium.
Istituto per le Applicazioni del Calcolo M.Picone sez. Bari, CNR, via G. Amendola 122/D, I-70126 Bari, Italy.
(literal)
- Titolo
- Solving linear systems with a Levinson-like solver (literal)
- Abstract
- 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 $ (p_1,p_2)$-Levinson conform matrices. This class incorporates, for instance, semiseparable, band, companion, arrowhead and many other matrices. For this class, we will derive a solver of complexity $O(p_1 p_2 n).$
The system solver is written inductively, and uses in every step k, the solution of a so-called
$k$-th order Yule-Walker-like equation. The algorithm obtained first has complexity algorithm $O(p_1 p_2 n^2).$ Based, however
on the specific structure of the simple $ (p_1,p_2)$-Levinson conform matrices, we will be able to further reduce the
complexity of the presented method, and get an order $O(p_1 p_2 n)$ algoritm.
Different examples of matrices are given for this algorithm. Examples are presented for: general dense matrices, upper triangular matrices, higher order generator semiseparable matrices, quasiseparable matrices, Givens-vector representable semiseparable matrices, band matrices, companion matrices, confederate matrices, arrowhead matrices, fellow matrices and many more.
Finally, the relation between this method and an upper triangular factorization of the original matrix is given and also details concerning possible look ahead methods are presented. (literal)
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