On the inequivalence of bilinear algorithms for 3×3 matrix multiplication

Authors:
Jinsoo Oh;Jin Kim;Byung-Ro Moon
Affiliations:
Daum Communications, Jeju-do, 690-150, Republic of Korea;School of Computer Science and Engineering, Seoul National University, Seoul, 151-744, Republic of Korea;School of Computer Science and Engineering, Seoul National University, Seoul, 151-744, Republic of Korea
Venue:
Information Processing Letters
Year:
2013

Citing 3
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Noncomutative bilinear algorithms for 3x3 matrix multiplication

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Abstract

Since Laderman showed an algorithm for 3x3 matrix multiplication using 23 scalar multiplications, Johnson and McLoughlin used a numerical optimization and human controlled method to give two parameterized algorithms in which the coefficients are rational numbers. The algorithms are inequivalent to Laderman@?s one with respect to the transformation introduced by de Groote. We present a simple and fast numerical heuristic for finding valid algorithms. Then we show that many of the obtained algorithms are inequivalent to the published ones.