A non-commutative algorithm for multiplying a 3×4 matrix by a 4×7 matrix using 63 non-complex multiplications
Overview & Synopsis
The number of scalar multiplications required to multiply a $3\times4$ matrix by a $4\times7$ matrix was reduced from 66 in [11] to 63 in [9] by an algorithm over complex numbers. We propose an algorithm in 63 multiplications with only rational coefficients, hence removing the requirement that the base field for the arithmetic operations contains a square root of -1, while it still needs to contain an inverse of 2. It was derived from the latter one, under the action of an isotropy which happen to project the algorithm on the field of rational numbers. We also produce a straight line program of this algorithm.
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Document Information
| Document Title | A non-commutative algorithm for multiplying a 3×4 matrix by a 4×7 matrix using 63 non-complex multiplications |
|---|---|
| Author / Organization | Jean-Guillaume Dumas, Clément Pernet, Alexandre Sedoglavic |
| Subject & Discipline | Multidisciplinary Academic Open Research |
| Categories | Science & Mathematics |
| Publication Year | 2025 |
| License / Rights | Open Access / Creative Commons |
| Resource Verification | Listed PDF (Verification Pending) |
| Original Host Website |
HAL Open Science
(hal.science)
|
| File Format | application/pdf (Portable Document Format) |
| Language | EN |
| Catalog ID | DOC-206570 |
| Original Source Link | Visit Source Page on hal.science » |