A 58-Addition, Rank-23 Scheme for General 3x3 Matrix Multiplication
Data Structures and Algorithms
2025-12-29 v1
Abstract
This paper presents a new state-of-the-art algorithm for exact matrix multiplication over general non-commutative rings, achieving a rank-23 scheme with only 58 scalar additions. This improves the previous best additive complexity of 60 additions without a change of basis. The result was discovered through an automated search combining ternary-restricted flip-graph exploration with greedy intersection reduction for common subexpression elimination. The resulting scheme uses only coefficients from , ensuring both efficiency and portability across arbitrary fields. The total scalar operation count is reduced from 83 to 81.
Keywords
Cite
@article{arxiv.2512.21980,
title = {A 58-Addition, Rank-23 Scheme for General 3x3 Matrix Multiplication},
author = {A. I. Perminov},
journal= {arXiv preprint arXiv:2512.21980},
year = {2025}
}