New combinations of methods for the acceleration of matrix multiplications

AbstractThe paper is a systematic survey of recently developed methods for the acceleration of MM, matrix multiplication, with some attention to the connections between MM and other computational problems (Boolean MM, Direct Sum Conjecture or DSC). The techniques of trilinear aggregating, uniting and canceling, AUC, due to the author, give the exponent < 2.77614 and a small constant defining an upper bounds on the both complexities, of MM and Boolean MM. By combining AUC with other recent techniques due to Bini, Capovani, Lotti, Romani, Schönhage and Winograd, the exponent was recently reduced to less than 2.5161 by the price of a serious increase of the constant. The AUC techniques are used to disprove DSC over the class of any precision approximating (APA) algorithms and also over the class of all so far designed conventional bilinear algorithms for MM