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Localisation robuste et dénombrement de valeurs propres

Abstract : This article deals with the localization of eigenvalues of a large sparse and not necessarily symmetric matrix in a domain of the complex plane. It combines two studies carried out earlier. The first work deals with the effect of applying small perturbations on a matrix, and referred to as e -spectrum or pseudospectrum. The second study describes a procedure for counting the number of eigenvalues of a matrix in a region of the complex plain surrounded by a closed curve. The two methods are combined in order to share the LU factorization of the resolvent, that intervenes in the two methods, so as to reduce the cost. The codes obtained are parallelized.
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L.B. Nguenang, Emmanuel Kamgnia, Bernard Philippe. Localisation robuste et dénombrement de valeurs propres. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2015, 19, pp.24-42. ⟨hal-01300099⟩

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