ABSTRACT

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<sup>3</sup>/2 multiplications instead of the n<sup>3</sup>multiplications which the regular method necessitates.

INDEX TERMS

Index terms?Algorithm, inner product, matrix inversion, matrix multiplication, solution of linear equations.

CITATION

S. Winograd, "A New Algorithm for Inner Product," in

*IEEE Transactions on Computers*, vol. 17, no. , pp. 693-694, 1968.

doi:10.1109/TC.1968.227420

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