Matrix Multiplication Over Word-Size Modular Rings Using Approximate Formulas

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 article, we show a novel way to use the approximate formula in the special case where the ring is Z / p Z . In addition, we show an implementation à la FFLAS--FFPACK, where p is a word-size modulo, that improves on state-of-the-art Z / p Z matrix multiplication implementations.