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.

翻译：本研究考虑指数函数的有理逼近，设计了一种适用于Hermitian矩阵情况的矩阵指数计算方法。通过部分分式分解，我们获得了一种可并行化的算法，其计算过程简化为线性系统的独立求解。我们分析了舍入误差对算法精度的影响，并通过数值实验验证了该方法的有效性，同时与Krylov算法进行了性能比较。