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Communication Dans Un Congrès Année : 2021

The Tensor Rank of 5x5 Matrices Multiplication is Bounded by 98 andIts Border Rank by 89

Résumé

We present a non-commutative algorithm for the product of 3 x 5 by 5 x 5 matrices using 58 multiplications. This algorithm allows to construct a non-commutative algorithm for multiplying 5 x 5 (resp. 10 x 10, 15 x 15) matrices using 98 (resp. 686, 2088) multiplications. Furthermore, we describe an approximate algorithm that requires 89 multiplications and computes this product with an arbitrary small error.
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Dates et versions

hal-04285141 , version 1 (14-11-2023)

Identifiants

Citer

Alexandre Sedoglavic, Alexey Smirnov. The Tensor Rank of 5x5 Matrices Multiplication is Bounded by 98 andIts Border Rank by 89. ISSAC '21: International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint Petersburg, Russia. pp.345-351, ⟨10.1145/3452143.3465537⟩. ⟨hal-04285141⟩
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