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Mathematics > Numerical Analysis

arXiv:1804.02614 (math)
[Submitted on 8 Apr 2018 (v1), last revised 11 Nov 2018 (this version, v2)]

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

Authors:Arvind K. Saibaba
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Abstract:This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the exact and the approximate singular subspaces. Second, we derive bounds for the low-rank approximation in any unitarily invariant norm (including the Schatten-p norm). This generalizes the bounds for Spectral and Frobenius norms found in the literature. Third, we present bounds for the accuracy of the singular values. The bounds are structural in that they are applicable to any starting guess, be it random or deterministic, that satisfies some minimal assumptions. Specialized bounds are provided when a Gaussian random matrix is used as the starting guess. Numerical experiments demonstrate the effectiveness of the proposed bounds.
Comments: 25 pages, 4 figures. Accepted, SIAM Journal on Matrix Analysis and Applications
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1804.02614 [math.NA]
  (or arXiv:1804.02614v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1804.02614

Submission history

From: Arvind Saibaba [view email]
[v1] Sun, 8 Apr 2018 02:22:00 UTC (226 KB)
[v2] Sun, 11 Nov 2018 19:19:59 UTC (119 KB)
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