Field extension and trilinear aggregating, uniting and canceling for the acceleration of matrix multiplications

Abstract

The acceleration of matrix multiplication MM, is based on the combination of the method of algebraic field extension due to D. Bini, M. Capovani, G. Lotti, F. Romani and S. Winograd and of trilinear aggregating, uniting and canceling due to the author. A fast algorithm of O(N2.7378) complexity for N × N matrix multiplication is derived. With A. Schönhage's Theorem about partial and total MM, our approach gives the exponent 2.6054 by the price of a serious increase of the constant.