A Note on Random Sampling for Matrix Multiplication
For practitioners of matrix multiplication, this offers an alternative sampling strategy that can yield better 2-norm accuracy in specific scenarios, though the improvement is incremental.
This paper extends randomised matrix multiplication to a coarser partition, proposing an algorithm that improves approximation error in 2-norm when the optimal distribution is near-uniform, while maintaining comparable Frobenius norm error bounds.
This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is closed to uniform. The new algorithm increases the likelihood of getting a small approximation error in 2-norm and has the squared approximation error in Frobenious norm bounded by that from the classical algorithm.