A 58-Addition, Rank-23 Scheme for General 3x3 Matrix Multiplication

Perminov Andrew

A 58-Addition, Rank-23 Scheme for General 3x3 Matrix Multiplication: 3 upvotes on Hugging Face Daily Papers, #14 of 15 papers on 2025-12-29. Day-by-day upvote history.

This paper presents a new state-of-the-art algorithm for exact 3times3 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 {-1, 0, 1}, ensuring both efficiency and portability across arbitrary fields. The total scalar operation count is reduced from 83 to 81.

Paper page on Hugging Face · arXiv

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