Volume 58, pp. 164-176, 2023.

Explicit deflation in Golub-Kahan-Lanczos bidiagonalization methods

James Baglama and Vasilije Perović


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.

Full Text (PDF) [494 KB], BibTeX

Key words

Lanczos bidiagonalization, (partial/truncated) singular value decomposition, deflation, thresholding

AMS subject classifications

65F15, 65F50, 15A18

Links to the cited ETNA articles

[24]Vol. 42 (2014), pp. 197-221 Qiao Liang and Qiang Ye: Computing singular values of large matrices with an inverse-free preconditioned Krylov subspace method

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