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Methods of conjugate gradients for solving linear systems
Open accessAbstract
An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns. The solution is given in n steps. It is shown that this method is a special case of a very general method which also includes Gaussian elimination. These general algorithms are essentially algorithms for finding an n dimensional ellipsoid. Connections are made with the theory of orthogonal polynomials and continued fractions.
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“Among the well-known formulas for β t , one may cite the Fletcher-Reeves [404], the Polak-Ribi`ere [405], the Polak-Ribi`ere-Polyak [406] and the Hestenes-Stiefel [407].”
MethodZhou, W., Nielsen, J. B., Fritsche, L. G., Dey, R., Gabrielsen, M. E., Wolford, B. N., LeFaive, J., VandeHaar, P., Gagliano, S. A., Gifford, A., et al. (2018) · Nature Genetics · doi:10.1038/s41588-018-0184-y · Cited by 1,544
Metadata
- Authors
- Hestenes, M. R., & Stiefel, E.
- Venue
- Journal of Research of the National Bureau of Standards
- Published
- 1952-12
- Volume
- 49
- Issue
- 6
- Pages
- 409
- ISSN
- 0091-0635 (ISSN-L)
- OpenAlex
- W2316564661
- Cited by
- 8,132
- References
- 0
- FWCI
- 12.48
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Hestenes, M. R., & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards. https://doi.org/10.6028/jres.049.044
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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