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Theses

Sur les méthodes rapides de résolution de systèmes de Toeplitz bandes

Abstract : This thesis aims to design new fast algorithms for numerical computation via the Toeplitz matrices. First, we introduced a fast algorithm to compute the inverse of a triangular Toeplitz matrix with real and/or complex numbers based on polynomial interpolation techniques. This algorithm requires only two FFT (2n) is clearly effective compared to predecessors. A numerical accuracy and error analysis is also considered. Numerical examples are given to illustrate the effectiveness of our method. In addition, we introduced a fast algorithm for solving a linear banded Toeplitz system. This new approach is based on extending the given matrix with several rows on the top and several columns on the right and to assign zeros and some nonzero constants in each of these rows and columns in such a way that the augmented matrix has a lower triangular Toeplitz structure. Stability of the algorithm is discussed and its performance is showed by numerical experiments. This is essential to connect our algorithms to applications such as image restoration applications, a key area in applied mathematics.
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Marwa Dridi. Sur les méthodes rapides de résolution de systèmes de Toeplitz bandes. Mathématiques générales [math.GM]. Université du Littoral Côte d'Opale; École nationale d'ingénieurs de Tunis (Tunisie), 2016. Français. ⟨NNT : 2016DUNK0402⟩. ⟨tel-01340838⟩

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