We present a new method for accelerating matrix multiplication asymptotically by using the Salem-Spencer Theorem, which gives a fairly dense set of integers with no three-term arithmetic progression.Expand

New algorithms for computing the Discrete Fourier Transform of n points are described. For n in the range of a few tens to a few thousands these algorithms use substantially fewer multiplications… Expand

A set equations in the quantities <italic>a<subscrpt>i</subscRpt></italic>(<italic_>p</italic>) and <italIC>q</ Italic> of lattice points in a system of uniform recurrence equations, in which the directed edges are labeled with integer vectors, is called a System of Uniform Recurrence Equations.Expand

Three examples General background Product of polynomials FIR filters Product of polynomials modulo a polynomial Cyclic convolution and discrete Fourier transform.

Several fast algorithms for computing discrete cosine transforms (DCTs) and their inverses on multidimensional inputs of sizes which are powers of 2 are introduced.Expand

Abstract The two main results of this note are: (i) The minimum number of multiplications required to multiply two 2 X 2 matrices is seven. (ii) The minimum number of multiplications/divisions… Expand

In this note we describe a new way of computing the inner product of two vectors using roughly n3/2 multiplications instead of the n3multiplications which the regular method necessitates.Expand

Construction of algorithms is a time honored mathematical activity. Euclid's algorithm for finding the greatest common divisor of two integers, as well as the many constructions by a ruler and… Expand