  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.
