Non-Euclidean geometrical aspects of the Schur and Levinson-Szegö algorithms - Archive ouverte HAL
Article Dans Une Revue IEEE Transactions on Information Theory Année : 2003

Non-Euclidean geometrical aspects of the Schur and Levinson-Szegö algorithms

Résumé

In this paper, we address non-Euclidean geometrical aspects of the Schur and Levinson-Szegö algorithms.We first show that the Lobachevski geometry is, by construction, one natural geometrical environment of these algorithms, since they necessarily make use of automorphisms of the unit disk. We next consider the algorithms in the particular context of their application to linear prediction. Then the Schur (resp., Levinson-Szegö) algorithm receives a direct (resp., polar) spherical trigonometry (ST) interpretation, which is a new feature of the classical duality of both algorithms
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Dates et versions

hal-01347779 , version 1 (21-07-2016)

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François Desbouvries. Non-Euclidean geometrical aspects of the Schur and Levinson-Szegö algorithms. IEEE Transactions on Information Theory, 2003, 49 (8), pp.1992 - 2003. ⟨10.1109/TIT.2003.814478⟩. ⟨hal-01347779⟩
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