The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
Abstract
This paper surveys perturbation theory for the pseudo–inverse (Moore–Penrose generalized inverse), for the orthogonal projection onto the column space of a matrix, and for the linear least squares problem.
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Citations
Cites
Perturbation Theory for Linear Operators
Kato, T. (1995) · Classics in Mathematics · doi:10.1007/978-3-642-66282-9 · Cited by 16,290
Solving Least Squares Problems
Lawson, C. L., & Hanson, R. J. (1995) · doi:10.1137/1.9781611971217 · Cited by 7,103
The algebraic eigenvalue problem
Wilkinson, J. H. (1965) · Cited by 5,833
The Algebraic Eigenvalue Problem
I., E., & Wilkinson, J. H. (1966) · Mathematics of Computation · doi:10.2307/2003558 · Cited by 5,140
A generalized inverse for matrices
Penrose, R. (1955) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100030401 · Cited by 4,551
Generalized Inverses: Theory and Applications
Rohatgi, V. K., Ben-Israel, A., & Greville, T. N. E. (1976) · International Statistical Review / Revue Internationale de Statistique · doi:10.2307/1403291 · Cited by 4,506
Perturbation theory for linear operators
Kato, T. (1966) · Springer eBooks · doi:10.1007/978-3-642-53393-8 · Cited by 2,611
Introduction to matrix computations
Stewart, G. W. (1973) · International Linear Collider · Cited by 2,381
Self-citationGeneralized Inverse of Matrices and Its Applications
Banerjee, K. S. (1973) · Technometrics · doi:10.1080/00401706.1973.10489026 · Cited by 2,310
Introduction to the Theory of Linear Non-selfadjoint Operators
Gohberg, I. (1969) · Medical Entomology and Zoology · Cited by 1,565
Cited by
The singular value decomposition: Its computation and some applications
Klema, V., & Laub, A. (1980) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1980.1102314 · Cited by 1,631
On the Early History of the Singular Value Decomposition
Stewart, G. W. (1993) · SIAM Review · doi:10.1137/1035134 · Cited by 985
Self-citationWampler, C. (1986) · IEEE Transactions on Systems, Man, and Cybernetics · doi:10.1109/tsmc.1986.289285 · Cited by 850
Separable nonlinear least squares: the variable projection method and its applications
Golub, G., & Pereyra, V. (2003) · Inverse Problems · doi:10.1088/0266-5611/19/2/201 · Cited by 760
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
Dolgov, S. V., & Savostyanov, D. V. (2014) · SIAM Journal on Scientific Computing · doi:10.1137/140953289 · Cited by 253
Metadata
- Authors
- Stewart, G. W.
- Venue
- SIAM Review
- Published
- 1977-10
- Volume
- 19
- Issue
- 4
- Pages
- 634-662
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2023782398
- Cited by
- 416
- References
- 24
- FWCI
- 6.48
- Type
- journal article
- Language
- en
- Open access
- closed
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- Stewart, G. W. (1977). On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems. SIAM Review. https://doi.org/10.1137/1019104
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.
