Fast Matrix Multiplication with Sketching

TL;DR

This paper introduces an approximate matrix multiplication algorithm using sketching techniques that reduces computational costs while maintaining accuracy, especially effective when the sample size is large.

Contribution

It proposes a novel matrix sketching-based algorithm that achieves comparable accuracy to existing methods with lower computational complexity for large samples.

Findings

Achieves similar accuracy bounds as state-of-the-art algorithms

Reduces computational cost in large sample regimes

Effective for approximate matrix multiplication tasks

Abstract

We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated using the sparsified matrix. We prove when the sample number grows large compared to the sample dimensions the proposed algorithm achieves similar accuracy bound with a smaller computational cost compared to the state-of-the-art algorithms.