We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function. This contrasts with the "classical" Monte Carlo method which only works with one entry at a time, resulting in a significant better convergence rate than the "classical" approach. To assess the applicability of our method, we compute the subgraph centrality and total communicability of several large networks. In all benchmarks analyzed so far, the performance of our method was significantly superior to the competition, being able to scale up to 64 CPU cores with a remarkable efficiency.

翻译：我们提出了一种新颖的随机算法，该算法通过随机抽样矩阵的整行和整列来逼近任意矩阵函数。这与“经典”蒙特卡罗方法每次仅处理一个矩阵元素形成对比，使得我们的算法收敛速度显著优于传统方法。为评估该方法的适用性，我们计算了多个大型网络的子图中心性和总通信性。在目前分析的所有基准测试中，我们的方法性能显著优于竞争方法，并且能够以卓越的效率扩展到64个CPU核心。