We present in this paper a new method based on Bernoulli matrix polynomials to approximate the exponential of a matrix. The developed method has given rise to two new algorithms whose efficiency and precision are compared to the most efficient implementations that currently exist. For that, a state-of-the-art test matrix battery, that allows deeply exploring the highlights and downsides of each method, has been used. Since the new algorithms proposed here do make an intensive use of matrix products, we also provide a GPUs-based implementation that allows to achieve a high performance thanks to the optimal implementation of matrix multiplication available on these devices.

我们在本文中提出了一种基于伯努利矩阵多项式来逼近矩阵指数的新方法。所开发的方法产生了两种新算法，它们的效率和精度与当前最有效的实现方案相比。为此，使用了先进的测试矩阵电池，该电池可以深入探索每种方法的亮点和缺点。由于此处提出的新算法确实大量使用了矩阵产品，因此我们还提供了基于GPU的实现，这是由于这些设备上可用的矩阵乘法的最佳实现而可以实现高性能。