{"ID":2824988,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.21980","arxiv_id":"2512.21980","title":"A 58-Addition, Rank-23 Scheme for General 3x3 Matrix Multiplication","abstract":"This paper presents a new state-of-the-art algorithm for exact $3\\times3$ 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.","short_abstract":"This paper presents a new state-of-the-art algorithm for exact $3\\times3$ 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 a...","url_abs":"https://arxiv.org/abs/2512.21980","url_pdf":"https://arxiv.org/pdf/2512.21980v1","authors":"[\"A. I. Perminov\"]","published":"2025-12-26T10:58:54Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[\"LoRA\"]","has_code":false}