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Some efficient methods for computing the determinant of large sparse matrices

Abstract : The computation of determinants intervenes in many scientific applications, as for example in the localization of eigenvalues of a given matrix A in a domain of the complex plane. When a procedure based on the application of the residual theorem is used, the integration process leads to the evaluation of the principal argument of the complex logarithm of the function g(z) = det((z + h)I - A)/ det(zI - A), and a large number of determinants is computed to insure that the same branch of the complex logarithm is followed during the integration. In this paper, we present some efficient methods for computing the determinant of a large sparse and block structured matrix. Tests conducted using randomly generated matrices show the efficiency and robustness of our methods.
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Emmanuel Kamgnia, Louis Bernard Nguenang. Some efficient methods for computing the determinant of large sparse matrices. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2014, Volume 17 - 2014 - Special issue CARI'12, pp.73-92. ⟨10.46298/arima.1968⟩. ⟨hal-01300060⟩

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