On the Eecient Use of Givens Rotations in Svd-based Subspace Tracking Algorithms ?

نویسنده

  • Philippe A. Pango
چکیده

In this paper, the issue of the eecient use of Givens rotations in SVD-based QR Jacobi-type subspace tracking algorithms is adressed. By relaxing the constraint of upper-triangularity on the singular value matrix, we show how even fewer Givens rotations can achieve a better diagonalization and provide more accurate singular values. Then, we investigate the eecient use of Givens rotations as a vector rotation tool. The cancellation of cross-terms is presented as an eecient signal/noise separation technique which guarantees a better updating of the subspaces basis. Regarding the choice between inner and outer rotations, we properly use the permutation properties of Givens rotations to maintain the non-increasing ordering of the singular values throughout the updating process, and analyse the consequences on the tracking performance of QR Jacobi-type algorithms. Finally, based on the developped theory, we propose two eecient subspace tracking algorithms which out-perform existing QR Jacobi-type algorithms. Comparative simulation experiments validate the concepts. R esum e Dans cet article, nous abordons le probl eme de l'utilisation optimale des rotations de Givens dans les algorithmes de type QR Jacobi pour le suivi de sous-espaces. En enlevant la contrainte de triangularit e sup erieure, nous montrons comment un nombre r eduit de rotations de Givens rotations peuvent produire une meilleure di-agonalisation de la matrice des valeurs singuli eres et donner des valeurs singuli eres plus pr ecises. Puis, nous analysons l'utilisation eecace des rotations de Givens en tant qu'outils de rotation de vecteurs. L'annulation des termes crois es est pr esen-t ee comme une technique eecace de s eparation des sous-espaces signal et bruit qui garantit une meilleure mise a jour des bases des sous-espaces. A propos du choix entre rotations internes et rotations externes, nous exploitons ad equatement les pro-pri et es permutatives de ces rotations pour maintenir l'ordre d ecroissant des valeurs singuli eres lors de la mise a jour, et analysons les cons equences sur les performances de suivi des algorithmes de type QR Jacobi. Finalement, en se basant sur la th eorie d evelopp ee, nous proposons deux algorithmes eecaces de suivi de sous-espaces dont les performances exc edent celles des algorithmes de type QR Jacobi existant. Des simulation exp erimentales valident les concepts propos es.

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تاریخ انتشار 1999