{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:34:50Z","timestamp":1787330090397,"version":"build-2736575974"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1720398"],"award-info":[{"award-number":["DMS-1720398"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1137\/18m1179432","type":"journal-article","created":{"date-parts":[[2019,1,8]],"date-time":"2019-01-08T15:45:51Z","timestamp":1546962351000},"page":"23-48","source":"Crossref","is-referenced-by-count":37,"title":["Randomized Subspace Iteration: Analysis of Canonical Angles and Unitarily Invariant Norms"],"prefix":"10.1137","volume":"40","author":[{"given":"Arvind K.","family":"Saibaba","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,1,8]]},"reference":[{"key":"atypb1","first-page":"347","author":"Avron H.","year":"2013","journal-title":"Proceedings of the International Conference on Machine Learning"},{"key":"atypb2","unstructured":"O. Balabanov and A. Nouy,\n                      Randomized Linear Algebra for Model Reduction. PartI: Galerkin Methods and Error Estimation\n                      , preprint,arXiv:1803.02602, 2018."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01600502"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"R. Bhatia,\n                      Matrix Analysis\n                      , Grad. Texts in Math. 169, Springer-Verlag, New York, 1997,https:\/\/doi.org\/10.1007\/978-1-4612-0653-8.","DOI":"10.1007\/978-1-4612-0653-8"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1973-0348991-3"},{"key":"atypb6","first-page":"40","author":"Boutsidis C.","year":"2015","journal-title":"Proceedings of the International Conference on Machine Learning"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"P. Drineas and I. C. F. Ipsen,\n                      Low-Rank Matrix Approximations Do Not Need a SIngular Value Gap\n                      , preprint,arXiv:1801.00670, 2018.","DOI":"10.1137\/18M1163658"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/16M1091745"},{"key":"atypb9","unstructured":"N. B. Erichson, S. L. Brunton, and J. N. Kutz,\n                      Randomized Dynamic Mode Decomposition\n                      , preprint,arXiv:1702.02912, 2017."},{"key":"atypb10","unstructured":"G. H. Golub and C. F. Van Loan,\n                      Matrix Computations\n                      , 4th ed., Johns Hopkins University Press, Baltimore, 2013."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/130938700"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/090771806"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-004-5244-2"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/140988541"},{"key":"atypb15","unstructured":"R. A. 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