The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
On the Compression of Low Rank Matrices
Abstract
A procedure is reported for the compression of rank-deficient matrices. A matrix A of rank k is represented in the form $A = U \circ B \circ V$, where B is a $k\times k$ submatrix of A, and U, V are well-conditioned matrices that each contain a $k\times k$ identity submatrix. This property enables such compression schemes to be used in certain situations where the singular value decomposition (SVD) cannot be used efficiently. Numerical examples are presented.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Golub, G. H., & Loan, C. F. V. (1996) · Johns Hopkins University Press eBooks · Cited by 6,027
Fast wavelet transforms and numerical algorithms I
Beylkin, G., Coifman, R., & Rokhlin, V. (1991) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160440202 · Cited by 1,770
Self-citationA new version of the Fast Multipole Method for the Laplace equation in three dimensions
Greengard, L., & Rokhlin, V. (1997) · Acta Numerica · doi:10.1017/s0962492900002725 · Cited by 879
Self-citationEfficient Algorithms for Computing a Strong Rank-Revealing QR Factorization
Gu, M., & Eisenstat, S. C. (1996) · SIAM Journal on Scientific Computing · doi:10.1137/0917055 · Cited by 677
Stewart, G. W. (1998) · Cited by 383
Numerics of Gram-Schmidt orthogonalization
Björck, Å. (1994) · Linear Algebra and its Applications · doi:10.1016/0024-3795(94)90493-6 · Cited by 320
Cited by
Randomized algorithms for the low-rank approximation of matrices
Liberty, E., Woolfe, F., Martinsson, P.-G., Rokhlin, V., & Tygert, M. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0709640104 · Cited by 559
Self-citationA fast randomized algorithm for the approximation of matrices
Woolfe, F., Liberty, E., Rokhlin, V., & Tygert, M. (2008) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2007.12.002 · Cited by 280
Self-citation
Metadata
- Authors
- Cheng, H., Gimbutas, Z., Martinsson, P. G., & Rokhlin, V.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2005-01
- Volume
- 26
- Issue
- 4
- Pages
- 1389-1404
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2038922352
- Cited by
- 301
- References
- 7
- FWCI
- 5.33
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: On the Compression of Low Rank Matrices. https://app.cochat.ai/papers/10.1137/030602678
- The paper
- Cheng, H., Gimbutas, Z., Martinsson, P. G., & Rokhlin, V. (2005). On the Compression of Low Rank Matrices. SIAM Journal on Scientific Computing. https://doi.org/10.1137/030602678
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
