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A Tutorial on the SWEEP Operator
Abstract
The importance of the SWEEP operator in statistical computing is not so much that it is an inversion technique, but rather that it is a conceptual tool for understanding the least squares process. The SWEEP operator can be programmed to produce generalized inverses and create, as by-products, such items as the Forward Doolittle matrix, the Cholesky decomposition matrix, the Hermite canonical form matrix, the determinant of the original matrix, Type I sums of squares, the error sum of squares, a solution to the normal equations, and the general form of estimable functions. First, this tutorial describes the use of Gauss-Jordan elimination for least squares and continues with a description of a completely generalized sweep operator that computes and stores (X′X)−, (X′X)− X′X, (X′X)− X′Y, and Y′Y — Y′X(X′X)− X′Y, all in the space of a single upper triangular matrix.
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Cited by
Palarea-Albaladejo, J., & Martín-Fernández, J. A. (2015) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2015.02.019 · Cited by 965
Graham, J. W., Hofer, S. M., & MacKinnon, D. P. (1996) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3102_3 · Cited by 366
Estimating variance components in a class of mixed models by restricted maximum likelihood
Smith, S. P., & Graser, H.-U. (1986) · Journal of Dairy Science · doi:10.3168/jds.s0022-0302(86)80516-1 · Cited by 247
Metadata
- Authors
- Goodnight, J. H.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 1979-08
- Volume
- 33
- Issue
- 3
- Pages
- 149-158
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W1964867919
- Cited by
- 174
- References
- 0
- FWCI
- 3.92
- Type
- journal article
- Language
- en
- Open access
- closed
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