期刊
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
卷 40, 期 1, 页码 23-48出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1179432
关键词
singular value decomposition; randomized algorithms; canonical angles; low-rank approximation
资金
- NSF [DMS 1720398]
This paper analyzes 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.
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