The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
The Geometry of Algorithms with Orthogonality Constraints
Abstract
In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms. It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.
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Cites
Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Sequential quadratic programming
Boggs, P. T., & Tolle, J. W. (1995) · Acta Numerica · doi:10.1017/s0962492900002518 · Cited by 1,858
Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten
Stiefel, E. (1935) · Commentarii Mathematici Helvetici · doi:10.1007/bf01199559 · Cited by 233
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Lotte, F., Bougrain, L., Cichocki, A., Clerc, M., Congedo, M., Rakotomamonjy, A., & Yger, F. (2018) · Journal of Neural Engineering · doi:10.1088/1741-2552/aab2f2 · Cited by 2,239
Hill, D. L. G., Batchelor, P. G., Holden, M., & Hawkes, D. J. (2001) · Physics in Medicine and Biology · doi:10.1088/0031-9155/46/3/201 · Cited by 2,093
Riemann manifold langevin and hamiltonian monte carlo methods
Girolami, M., & Calderhead, B. (2011) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2010.00765.x · Cited by 1,473
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Wolf, L., Hassner, T., & Maoz, I. (2011) · CVPR 2011 · doi:10.1109/cvpr.2011.5995566 · Cited by 1,382
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Lipp, T., & Boyd, S. (2016) · Optimization and Engineering · doi:10.1007/s11081-015-9294-x · Cited by 744
Metadata
- Authors
- Edelman, A., Arias, T. A., & Smith, S. T.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 1998-01
- Volume
- 20
- Issue
- 2
- Pages
- 303-353
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2045512849
- Cited by
- 2,685
- References
- 4
- FWCI
- 24.61
- Type
- journal article
- Language
- en
- Open access
- closed
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- Edelman, A., Arias, T. A., & Smith, S. T. (1998). The Geometry of Algorithms with Orthogonality Constraints. SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/s0895479895290954
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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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