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This survey explores modern approaches for computing low-rank approximationsof high-dimensional matrices by means of the randomized SVD, randomizedsubspace iteration, and randomized block Krylov iteration. The paper comparesthe procedures via theoretical analyses and numerical studies to highlight howthe best choice of algorithm depends on spectral properties of the matrix andthe computational resources available.  Despite superior performance for many problems, randomized block Kryloviteration has not been widely adopted in computational science. The paperstrengthens the case for this method in three ways. First, it presents newpseudocode that can significantly reduce computational costs. Second, itprovides a new analysis that yields simple, precise, and informative errorbounds. Last, it showcases applications to challenging scientific problems,including principal component analysis for genetic data and spectral clusteringfor molecular dynamics data.

Randomized algorithms for low-rank matrix approximation: Design, analysis, and applications