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The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations
Abstract
This paper presents a more detailed analysis of a class of minimization algorithms, which includes as a special case the DFP (Davidon-Fletcher-Powell) method, than has previously appeared. Only quadratic functions are considered but particular attention is paid to the magnitude of successive errors and their dependence upon the initial matrix. On the basis of this a possible explanation of some of the observed characteristics of the class is tentatively suggested.
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Cited by
te Velde, G., Bickelhaupt, F. M., Baerends, E. J., Fonseca Guerra, C., van Gisbergen, S. J. A., Snijders, J. G., & Ziegler, T. (2001) · Journal of Computational Chemistry · doi:10.1002/jcc.1056 · Cited by 10,152
Using redundant internal coordinates to optimize equilibrium geometries and transition states
Peng, C., Ayala, P. Y., Schlegel, H. B., & Frisch, M. J. (1996) · Journal of Computational Chemistry · doi:10.1002/(sici)1096-987x(19960115)17:1<49::aid-jcc5>3.0.co;2-0 · Cited by 2,749
The Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031
Zhou, L., Wang, S.-T., Choi, S., Pichler, H., & Lukin, M. D. (2020) · Physical Review X · doi:10.1103/physrevx.10.021067 · Cited by 913
Improved Peptide and Protein Torsional Energetics with the OPLS-AA Force Field
Robertson, M. J., Tirado-Rives, J., & Jorgensen, W. L. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00356 · Cited by 854
Metadata
- Authors
- BROYDEN, C. G.
- Venue
- IMA Journal of Applied Mathematics
- Publisher
- Oxford University Press (OUP)
- Published
- 1970
- Volume
- 6
- Issue
- 1
- Pages
- 76-90
- ISSN
- 0272-4960 (ISSN-L)
- 1464-3634
- OpenAlex
- W2103111465
- Cited by
- 2,874
- References
- 0
- FWCI
- 2.43
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations. https://app.cochat.ai/papers/10.1093/imamat/6.1.76
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- BROYDEN, C. G. (1970). The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations. IMA Journal of Applied Mathematics. https://doi.org/10.1093/imamat/6.1.76
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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.
