Improved basis-change transformations for $2 \times 2$ matrix multiplication
To the best of our knowledge, we present a state-of-the-art change-of-basis algorithm for $2 \times 2$ matrix multiplication under the Karstadt--Schwartz-style basis change regime [1]. We do this by introducing basis-change matrices $B_U$, $B_V$, and $B_W$ that each require only a single addition and hence give rise to a matrix-multiplication algorithm performing $5n^{\log_2{7}} - 4n^2 + \frac{3}{4}n^2 \log_2{n},$ arithmetic operations when multiplying two $n \times n$ matrices, with $n$ a power of $2$. This improves on the previous best bound, which had last term $\frac{3}{2}n^2\log_2{n}$.
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00671
curl -X POST /api/v1/records/hexagon/2610.00671/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00671/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'