Augmented Implicitly Restarted Lanczos Bidiagonalization Methods

By James Baglama, Lothar Reichel. SIAM Journal on Scientific Computing, 2005

357 citations recorded by the source corpus.

New restarted Lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented. Restarting is carried out by augmentation of Krylov subspaces that arise naturally in the standard Lanczos bidiagonalization method. The augmenting vectors are associated with certain Ritz or harmonic Ritz vectors. Computed examples show the new methods to be competitive with available schemes.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cea471f48dc4f915e75966e6ad13190d92e9b64d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Peter Bhlmann
2. J. Nathan Kutz
3. M. J. van der Laan
4. Sergey Voronin
5. Petros Drineas
6. Martin Stoll
7. Michael J. Kane
8. N. Benjamin Erichson

In Computational Theory and Mathematics

1. Steven L. Brunton
2. J. Nathan Kutz
3. Peter Bhlmann
4. Michael J. Kane
5. M. J. van der Laan
6. Sergey Voronin
7. Petros Drineas
8. Martin Stoll

In Statistical and Nonlinear Physics

1. Steven L. Brunton
2. J. Nathan Kutz
3. Maizar Raissi
4. Joshua L. Proctor
5. Peter Bhlmann
6. Andrew W. Butler
7. M. J. van der Laan
8. Sergey Voronin

Citations in the corpus

• Randomized Matrix Decompositions using R (2016, methodology): “The most competitive partial SVD routines in R are provided by the svd (Korobeynikov and Larsen 2016), RSpectra (Qiu, Mei, Guennebaud, and Niesen 2016), and the irlba (Baglama and Reichel 2005) packages.”
• Handbook of Big Data (2016, methodology): “This method will not be described in this chapter since our focus is in the context of large data and on computing the largest singular triplets; therefore, we refer the reader to [1] for details on irlba(H).”
• A Krylov–Schur approach to the truncated SVD (2012, methodology): “Both kssvd and Baglama and Reichel's method use a one-sided reorthogonalization process.”
• Integrating single-cell transcriptomic data across different conditions, technologies, and species (2018, methodology): “Since we are interested in only a subset of the canonical correlation vectors, we approximated the singular value decomposition with a partial singular value decomposition using the augmented implicitly restarted Lanczos bidiagonali-zation algorithm implemented in the irlba R package 61 .”
• Reversed graph embedding resolves complex single-cell developmental trajectories (2017, methodology): “ICA is based on ica helper function from Monocle package where ica helper function is built on irlba package [11].”