Strassen's algorithm not optimal trilinear technique of aggregating, Uniting and canceling for constructing fast algorithms for matrix operations

Abstract

A new technique of trilinear operations of aggregating, uniting and canceling is introduced and applied to constructing fast linear non-commutative algorithms for matrix multiplication. The result is an asymptotic improvement of Strassen's famous algorithms for matrix operations. Key words: fast algorithms, complexity of computation, arithmetic complexity, linear algebraic problems, matrix multiplication, bilinear forms, trilinear form.