New ways to multiply 3 × 3-matrices
| Autor: | Martina Seidl, Marijn J. H. Heule, Manuel Kauers |
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| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory 010102 general mathematics Dimension (graph theory) 010103 numerical & computational mathematics 01 natural sciences law.invention Set (abstract data type) Computational Mathematics law Product (mathematics) 0101 mathematics Manifold (fluid mechanics) Mathematics |
| Zdroj: | Journal of Symbolic Computation. 104:899-916 |
| ISSN: | 0747-7171 |
| DOI: | 10.1016/j.jsc.2020.10.003 |
| Popis: | It is known since the 1970s that no more than 23 multiplications are required for computing the product of two 3 × 3 -matrices. For non-commutative coefficient rings, it is not known whether it can also be done with fewer multiplications. However, there are several mutually inequivalent ways of doing the job with 23 multiplications. In this article, we extend this list considerably by providing more than 17,000 new and mutually inequivalent schemes for multiplying 3 × 3 -matrices using 23 multiplications. Moreover, we show that the set of all these schemes is a manifold of dimension at least 17. |
| Databáze: | OpenAIRE |
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