Matrix multiplication via arithmetic progressions

  • Authors:
  • Don Coppersmith;Shmuel Winograd

  • Affiliations:
  • -;-

  • Venue:
  • Journal of Symbolic Computation - Special issue on computational algebraic complexity
  • Year:
  • 1990

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Abstract

We present a new method for accelerating matrix multiplication asymptotically. Thiswork builds on recent ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product. We make novel use of the Salem-Spencer Theorem, which gives a fairly dense set of integers with no three-term arithmetic progression. Our resulting matrix exponent is 2.376.