Matrix multiplication over word-size modular rings using approximate formulae

Abstract : Bini–Capovani–Lotti–Romani approximate formula (or border rank) for matrix multiplication achieves a better complexity than Strassen’s matrix multiplication formula. In this paper, we show a novel way to use the approximate formula in the special case where the ring is Z/pZ. Besides, we show an implementation à la FFLAS–FFPACK, where p is a word-size modulo, that improves on state-of-the-art Z/pZ matrix multiplication implementations.
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Brice Boyer, Jean-Guillaume Dumas. Matrix multiplication over word-size modular rings using approximate formulae. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2016, 42 (3-20), ⟨10.1145/2829947⟩. ⟨hal-00987812⟩

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