  Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix
multiplication algorithm, based on a variant of Strassen's algorithm, and used
this to develop new algorithms for Boolean matrix multiplication, among other
tasks. Their algorithm can compute Boolean matrix multiplication in
$O(n^{2.778})$ time. While asymptotically faster matrix multiplication
algorithms exist, most such algorithms are infeasible for practical problems.
  We describe an alternative way to use the broken multiplication algorithm to
approximately compute matrix multiplication, either for real-valued or Boolean
matrices. In brief, instead of running multiple iterations of the broken
algorithm on the original input matrix, we form a new larger matrix by sampling
and run a single iteration of the broken algorithm on it. Asymptotically, our
algorithm has runtime $O(n^{2.763})$, a slight improvement over the
Karppa-Kaski algorithm.
  Since the goal is to obtain new practical matrix-multiplication algorithms,
we also estimate the concrete runtime for our algorithm for some large-scale
sample problems. It appears that for these parameters, further optimizations
are still needed to make our algorithm competitive.
