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This paper is concerned with the analysis of the randomized subspaceiteration for the computation of low-rank approximations. We present threedifferent kinds of bounds. First, we derive both bounds for the canonicalangles between the exact and the approximate singular subspaces. Second, wederive bounds for the low-rank approximation in any unitarily invariant norm(including the Schatten-p norm). This generalizes the bounds for Spectral andFrobenius norms found in the literature. Third, we present bounds for theaccuracy of the singular values. The bounds are structural in that they areapplicable to any starting guess, be it random or deterministic, that satisfiessome minimal assumptions. Specialized bounds are provided when a Gaussianrandom matrix is used as the starting guess. Numerical experiments demonstratethe effectiveness of the proposed bounds.

Randomized subspace iteration: Analysis of canonical angles and unitarily invariant norms