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，该算法通过随机采样矩阵的完整行和列，利用幂级数展开来逼近任意矩阵函数。这与仅能逐项操作的现有蒙特卡洛方法形成对比，从而实现了比原始方法显著更优的收敛速率。为评估本方法的适用性，我们计算了多个大型网络的子图中心性和总连通性。在所有已分析的基准测试中，本方法的性能显著优于同类方法，且能够高效扩展至64个CPU核心。