The DOI matches its Crossref record.
Numerical Linear Algebra
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“For a backward-stable evaluation, the standard perturbation bound of numerical linear algebra [32,33] gives a relative forward error”
From Curvature-Corrected Rotary Position Embeddings: An Entropy-Invariant Temperature for Mitigating Numerical-Rank Collapse in Long-Context Attention (2026) · cites this paper as [33]
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Mtetwa, J. T., Ogudo, K. A., & Pudaruth, S. (2026) · Mathematics · doi:10.3390/math14142637
“For a backward-stable evaluation, the standard perturbation bound of numerical linear algebra [32,33] gives a relative forward error so a condition number κ corresponds to a worst-case loss of about log 10 κ significant decimal digits.”
Metadata
- Authors
- Trefethen, L. N., & Bau, III
- Affiliations
- University of Oxford (GB)
- Microsoft Corporation
- ORCID
- Trefethen, Lloyd N.
- Venue
- Society for Industrial and Applied Mathematics eBooks
- Published
- 1997-01
- OpenAlex
- W4320800818
- Cited by
- 3,301
- References
- 0
- Citations by year
- 2026: 97 · 2025: 179 · 2024: 148 · 2023: 192 · 2022: 194 · 2021: 186 · 2020: 209 · 2019: 174 · 2018: 179 · 2017: 169 · 2016: 145 · 2015: 150 · 2014: 176 · 2013: 164 · 2012: 150
- FWCI
- 5.17
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Society for Industrial and Applied Mathematics eBooks (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
- Keywords
- numerical linear algebra, linear systems, eigenvalue problem, singular value decomposition, least squares, QR decomposition, LU decomposition, Cholesky decomposition, iterative methods
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.
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