Weighted sampling of outer products
نویسنده
چکیده
This note gives a simple analysis of the randomized approximation scheme for matrix multiplication of Drineas et al. (2006) with a particular sampling distribution over outer products. The result follows from a matrix version of Bernstein’s inequality. To approximate the matrix product AB⊤ to spectral norm error ε‖A‖‖B‖, it suffices to sample on the order of (sr(A) ∨ sr(B)) log(sr(A) ∧ sr(B))/ε outer products, where sr(M ) is the stable rank of a matrix M .
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ورودعنوان ژورنال:
- CoRR
دوره abs/1410.4429 شماره
صفحات -
تاریخ انتشار 2014