• Publications
  • Influence
Matrix multiplication via arithmetic progressions
TLDR
We present a new method for accelerating matrix multiplication asymptotically, by using a basic trilinear form which is not a matrix product. Expand
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  • 156
Matrix multiplication via arithmetic progressions
TLDR
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
  • 1,255
  • 99
  • PDF
On computing the Discrete Fourier Transform.
  • S. Winograd
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences…
  • 1976
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 multiplicationsExpand
  • 680
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  • PDF
The Organization of Computations for Uniform Recurrence Equations
TLDR
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
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  • PDF
Arithmetic complexity of computations
Three examples General background Product of polynomials FIR filters Product of polynomials modulo a polynomial Cyclic convolution and discrete Fourier transform.
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Fast algorithms for the discrete cosine transform
  • E. Feig, S. Winograd
  • Mathematics, Computer Science
  • IEEE Trans. Signal Process.
  • 1 September 1992
TLDR
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
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  • 25
On the Asymptotic Complexity of Matrix Multiplication
TLDR
The main results of this paper have the following flavor: Given one algorithm for multiplying matrices, there exists another, better, algorithm. Expand
  • 212
  • 20
On multiplication of 2 × 2 matrices
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/divisionsExpand
  • 207
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A New Algorithm for Inner Product
  • S. Winograd
  • Mathematics, Computer Science
  • IEEE Transactions on Computers
  • 1 July 1968
TLDR
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
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  • 10
Complexity Of Computations
  • S. Winograd
  • Computer Science
  • ACM Annual Conference
  • 4 December 1978
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 andExpand
  • 102
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