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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 164-176, 2023/02/07
We discuss a simple, easily overlooked, explicit deflation procedure applied to Golub-Kahan-Lanczos Bidiagonalization (GKLB)-based methods to compute the next set of the largest singular triplets of a matrix from an already computed partial singular value decomposition. Our results here complement the vast literature on this topic, provide additional insight, and highlight the simplicity and the effectiveness of this procedure. We demonstrate how existing GKLB-based routines for the computation of the largest singular triplets can be easily adapted to take advantage of explicit deflation, thus making it more appealing to a wider range of users. Numerical examples are presented including an application of singular value thresholding.
Keywords: Lanczos bidiagonalization, (partial/truncated) singular value decomposition, deflation, thresholding