Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations

Understand

Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices.

• The performance of such techniques has been extensively analyzed, and very precise estimates on the distribution of the residual errors have been derived.
• However, our understanding of the accuracy of the computed singular vectors (measured in terms of the canonical angles between the spaces spanned by the exact and the computed singular vectors, respectively) remains relatively limited.
• In this work, we present practical bounds and estimates for canonical angles of randomized subspace approximation that can be computed efficiently either a priori or a posteriori, without assuming prior knowledge of the true singular subspaces.