The tensor rank of 5x5 matrices multiplication is bounded by 98 and its border rank by 89

The tensor rank of 5x5 matrices multiplication is bounded by 98 and its border rank by 89

We present a non-commutative algorithm for the product of 3x5 by 5x5 matrices using 58 multiplications. This algorithm allows to construct a non-commutative algorithm for multiplying 5x5 (resp. 10x10, 15x15) matrices using 98 (resp. 686, 2088) multiplications. Furthermore, we describe an approximate...

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Veröffentlicht in:arXiv.org 2021-02
Hauptverfasser: Sedoglavic, Alexandre, Smirnov, Alexey V
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Multiplication
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description We present a non-commutative algorithm for the product of 3x5 by 5x5 matrices using 58 multiplications. This algorithm allows to construct a non-commutative algorithm for multiplying 5x5 (resp. 10x10, 15x15) 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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Tensors
title The tensor rank of 5x5 matrices multiplication is bounded by 98 and its border rank by 89
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