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Theses

Sur quelques algorithmes d'analyse de stabilité forte de matrices symplectiques

Abstract : The first chapter of this thesis presents some spectral properties of symplectic matrices and their link to strong stability. In particular, emphasis is placed on the most numerically useful properties which are used throughout the thesis. In the second chapter we propose an adaptation of spectral dichotomy algorithms to symplectic matrices. This adaptation allows us to find, in a stable way, the spectral projections onto the invariant subspaces associated with the eigenvalues inside, on and outside the unit circle. With these information, we propose an algorithm, based again on the spectral dichotomy techniques, to analyze the strong stability. In the third chapter, we propose another approach referred to as spectral trichotomy, for computing the abovementioned spectral projections. We analyse the convergence behavior of this algorithm and compare it with the approach proposed in chapter 2.
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Submitted on : Saturday, September 24, 2011 - 11:19:40 PM
Last modification on : Wednesday, September 16, 2020 - 9:56:31 AM
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Mouhamadou Dosso. Sur quelques algorithmes d'analyse de stabilité forte de matrices symplectiques. Mathématiques [math]. Université de Bretagne occidentale - Brest, 2011. Français. ⟨NNT : 0CPZR600AC2⟩. ⟨tel-00626273⟩

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