# Randomization of Approximate Bilinear Computation for Matrix Multiplication

## TL;DR

This paper introduces a randomization technique for approximate bilinear matrix multiplication formulas, improving performance in the presence of computational and approximation errors through theoretical analysis and experiments.

## Contribution

It proposes a novel randomization method for approximate bilinear formulas and analyzes its effectiveness under different error sources.

## Key findings

- Improved accuracy with randomization in approximate formulas
- Enhanced performance when combined with floating point arithmetic errors
- Theoretical and experimental validation of the method's benefits

## Abstract

We present a method for randomizing formulas for bilinear computation of matrix products. We consider the implications of such randomization when there are two sources of error: One due to the formula itself only being approximately correct, and one due to using floating point arithmetic. Our theoretical results and numerical experiments indicate that our method can improve performance when each of these error sources are present individually, as well as when they are present at the same time.