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Abstract—In this note we describe a new way of computing the inner product of two vectors. This method cuts down the number of multiplications required when we want to perform a large number of inner products on a smaller set of vectors. In particular, we obtain that the product of two n×n matrices can be performed using roughly n 3 /2 multiplications instead of the n 3 multiplications which the regular method necessitates.
S. Winograd (Mon,) studied this question.