The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Some Modified Matrix Eigenvalue Problems
Abstract
We consider the numerical calculation of several matrix eigenvalue problems which require some manipulation before the standard algorithms may be used. This includes finding the stationary values of a quadratic form subject to linear constraints and determining the eigenvalues of a matrix which is modified by a matrix of rank one. We also consider several inverse eigenvalue problems. This includes the problem of determining the coefficients for the Gauss–Radau and Gauss–Lobatto quadrature rules. In addition, we study several eigenvalue problems which arise in least squares.
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Citations
Cites
Singular value decomposition and least squares solutions
Golub, G. H., & Reinsch, C. (1970) · Numerische Mathematik · doi:10.1007/bf02163027 · Cited by 2,929
Self-citation
Cited by
An Analysis of the Total Least Squares Problem
Golub, G. H., & van Loan, C. F. (1980) · SIAM Journal on Numerical Analysis · doi:10.1137/0717073 · Cited by 1,753
Self-citationRecursive PCA for adaptive process monitoring
Li, W., Yue, H. H., Valle-Cervantes, S., & Qin, S. J. (2000) · Journal of Process Control · doi:10.1016/s0959-1524(00)00022-6 · Cited by 848
Tracking a few extreme singular values and vectors in signal processing
Comon, P., & Golub, G. H. (1990) · Proceedings of the IEEE · doi:10.1109/5.58320 · Cited by 489
Self-citationA survey of matrix inverse eigenvalue problems
Boley, D., & Golub, G. H. (1987) · Inverse Problems · doi:10.1088/0266-5611/3/4/010 · Cited by 223
Self-citationConstrained instruments and their application to Mendelian randomization with pleiotropy
Jiang, L., Oualkacha, K., Didelez, V., Ciampi, A., Rosa‐Neto, P., Benedet, A. L., Mathotaarachchi, S., Richards, J. B., Greenwood, C. M. T., & Initiative, A. F. T. A. D. N. (2019) · Genetic Epidemiology · doi:10.1002/gepi.22184 · Cited by 23
Metadata
- Authors
- Golub, G. H.
- Venue
- SIAM Review
- Published
- 1973-04
- Volume
- 15
- Issue
- 2
- Pages
- 318-334
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2105433369
- Cited by
- 728
- References
- 1
- FWCI
- 0.52
- Type
- journal article
- Language
- en
- Open access
- closed
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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.
