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We propose a new fast randomized algorithm for interpolative decomposition ofmatrices which utilizes CountSketch. We then extend this approach to the tensorinterpolative decomposition problem introduced by Biagioni et al. (J. Comput.Phys. 281, pp. 116-134, 2015). Theoretical performance guarantees are providedfor both the matrix and tensor settings. Numerical experiments on bothsynthetic and real data demonstrate that our algorithms maintain the accuracyof competing methods, while running in less time, achieving at least an orderof magnitude speed-up on large matrices and tensors.

Fast Randomized Matrix and Tensor Interpolative Decomposition Using CountSketch