A non-commutative algorithm for multiplying 5x5 matrices using 99 multiplications

TL;DR

This paper introduces a non-commutative algorithm for 5x5 matrix multiplication that reduces the number of multiplications from 100 to 99, improving the efficiency of matrix multiplication algorithms.

Contribution

It presents a novel modification of Makarov's algorithm achieving fewer multiplications for 5x5 matrices.

Findings

Achieves 99 multiplications for 5x5 matrix multiplication

Improves upon the previous best known bound of 100 multiplications

Demonstrates a minor but significant modification of existing algorithms

Abstract

We present a non-commutative algorithm for multiplying 5x5 matrices using 99 multiplications. This algorithm is a minor modification of Makarov's algorithm which exhibit the previous best known bound with 100 multiplications.