The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization
Abstract
It is shown that the basic regularization procedures for finding meaningful approximate solutions of ill-conditioned or singular linear systems can be phrased and analyzed in terms of classical linear algebra that can be taught in any numerical analysis course. Apart from rewriting many known results in a more elementary form, we also derive a new two-parameter family of merit functions for the determination of the regularization parameter. The traditional merit functions from generalized cross validation (GCV) and generalized maximum likelihood (GML) are recovered as special cases.
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Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Spline Models for Observational Data
Wahba, G. (1990) · doi:10.1137/1.9781611970128 · Cited by 4,184
Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
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Metadata
- Authors
- Neumaier, A.
- Venue
- SIAM Review
- Published
- 1998-01
- Volume
- 40
- Issue
- 3
- Pages
- 636-666
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2019787708
- Cited by
- 644
- References
- 3
- FWCI
- 12.60
- Type
- journal article
- Language
- en
- Open access
- closed
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- Neumaier, A. (1998). Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization. SIAM Review. https://doi.org/10.1137/s0036144597321909
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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.
