Toward an Algorithm for Fast Matrix Multiplication

The multiplication of two matrices is one of the most fundamental operations in linear algebra and in computational mathematics at large. The costs for the multiplication of two dense n x2;x n matrices is O(n3) operations. As such, it forms a bottle neck in many fields ranging from classical applications in scientific computing to recent areas such as Big Data. It is known that reducing the complexity for matrix multiplication would correspondingly also allow one to reduce the complexity of many other procedures in numerical mathematics, such as Gaussian elimination, LU decomposition, computing the determinant or the inverse of a matrix. Matrix multiplication is also used as a subroutine in a plethora of computational problems that, on the face of it, have nothing to do with matrices.