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Preprints, Working Papers, ... (Preprint) Year : 2023

Parallel approximation of the exponential of Hermitian matrices

Approximation parallèle de l'exponentielle de matrices Hermitiennes

Abstract

In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the computation reduces to independent resolutions of linear systems. We analyze the effects of rounding errors on the accuracy of our algorithm. We complete this work with numerical tests showing the efficiency of our method and a comparison of its performances with Krylov algorithms.
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Dates and versions

hal-03948509 , version 1 (20-01-2023)
hal-03948509 , version 2 (28-06-2023)

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Frédéric Hecht, Sidi-Mahmoud Kaber, Lucas Perrin, Alain Plagne, Julien Salomon. Parallel approximation of the exponential of Hermitian matrices. 2023. ⟨hal-03948509v2⟩
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