Matrix multiplication via arithmetic progressions

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. © 1990, Academic Press Limited. All rights reserved.