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 using the power series expansion. This contrasts with existing Monte Carlo methods, which only work with one entry at a time, resulting in a significantly better convergence rate than the original 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 remarkable efficiency.

翻译：我们提出了一种新颖的随机算法，通过随机采样矩阵的整行和整列，利用幂级数展开来逼近任意矩阵函数。这与现有的蒙特卡洛方法形成对比，后者每次仅处理一个矩阵元素，因此我们的方法收敛速度显著优于原始方法。为评估方法的适用性，我们计算了多个大型网络的子图中心性和总通信性。在所有已分析的基准测试中，我们的方法性能明显优于竞争对手，能够高效扩展至64个CPU核心，展现出卓越的可扩展性。