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：我们提出一种新颖的随机算法，该算法通过随机采样矩阵的整行与整列，利用幂级数展开逼近任意矩阵函数。这与现有仅逐元素操作的蒙特卡洛方法形成对比，从而实现了显著优于原始方法的收敛速率。为评估方法适用性，我们计算了多个大规模网络的子图中心性与总传播能力。在所有已分析的基准测试中，本方法性能显著超越同类算法，能够以卓越效率扩展至64个CPU核心。