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arXiv · 2212.01175

Flip Graphs for Matrix Multiplication

Manuel Kauers·Jakob Moosbauer
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Abstract

We introduce a new method for discovering matrix multiplication schemes based on random walks in a certain graph, which we call the flip graph. Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5), both in characteristic two and for arbitrary ground fields.

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Manuel Kauers, Jakob Moosbauer. 2022-12-02. Flip Graphs for Matrix Multiplication. https://arxiv.org/abs/2212.01175

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