In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To improve the practicability of the block sizes, two modified ones with less computation cost are provided. With respect to the second one, a two step algorithm is also devised. Moreover, the probability error bounds for the proposed algorithms are given. Extensive numerical results show that our methods outperform the existing one in the literature.

翻译：在本文中, 我们从随机抽样角度调查区块矩阵乘法的随机算法。 根据A- 最佳设计标准, 获得了最佳取样概率和取样区块大小。 为了提高区块大小的实用性, 提供了两个修改后算法, 计算成本较低。 关于第二个, 还设计了两个步骤算法。 此外, 给出了拟议算法的概率误差界限。 广泛的数字结果显示, 我们的方法超过了文献中的现有方法 。