Matrix multiplication over word-size modular rings using approximate formulae

Brice Boyer (1) , Jean-Guillaume Dumas (2)

1 Department of mathematics [North Carolina]
2 CASYS - Calculs Algébriques et Systèmes Dynamiques

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.

Mots clés: matrix multiplication; efficient implementation; Strassen-Winograd's algorithm; Bini's approximate bilinear algorithm; symbolic-numeric computing; memory placement and scheduling; exact linear algebra

Domaines: Calcul formel [cs.SC]

Brice Boyer, Jean-Guillaume Dumas. Matrix multiplication over word-size modular rings using approximate formulae. ACM Transactions on Mathematical Software, 2016, 42 (3-20), ⟨10.1145/2829947⟩. ⟨hal-00987812⟩