Algorithm 1:  Monte Carlo AMM [32]

Require:  $\mathit{A}\in {\mathbb{R}}^{m\times k}$ and $\mathit{B}\in {\mathbb{R}}^{k\times n}$, and $c\in \mathbb{N}$

Ensure: $\mathit{Z}\in {\mathbb{R}}^{m\times n}$ such that $\parallel \mathit{AB}-\mathit{Z}\parallel$ is small

1:   $\mathit{Z}\leftarrow \mathit{O}$

2:  Set $p_1,\dots ,p_k$ such that ${\sum }_{l=1}^k{p}_l=1$

3:  for $t=1,\dots ,c$  do

4:        Pick $i_t$ with $\mathbb{P}[i_t=l]=p_l$

5:        $\mathit{Z}\leftarrow \mathit{Z}+{\displaystyle \frac{{\mathit{A}}^{\left(i_t\right)}{\mathit{B}}_{\left(i_t\right)}}{c{p}_{i_t}}}$

6:  end for