The DOI matches its Crossref record; 49 of the 49 references it cites were found in a registry or an index.
Separable nonlinear least squares: the variable projection method and its applications
Open accessAbstract
In this paper we review 30 years of developments and applications of the variable projection method for solving separable nonlinear least-squares problems.These are problems for which the model function is a linear combination of nonlinear functions.Taking advantage of this special structure, the method of variable projections eliminates the linear variables obtaining a somewhat more complicated function that involves only the nonlinear parameters.This procedure not only reduces the dimension of the parameter space but also results in a better-conditioned problem.The same optimization method applied to the original and reduced problems will always converge faster for the latter.We present first a historical account of the basic theoretical work and its various computer implementations, and then report on a variety of applications from electrical engineering, medical and biological imaging, chemistry, robotics, vision, and environmental sciences.An extensive bibliography is included.The method is particularly well suited for solving real and complex exponential model fitting problems, which are pervasive in their applications and are notoriously hard to solve.
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Cites
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Trimmed constrained mixed effects models: formulations and algorithms
Zheng, P., Barber, R., Sorensen, R. J. D., Murray, C. J. L., & Aravkin, A. Y. (2021) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2020.1868303 · Cited by 174
Diffusion time dependence, power‐law scaling, and exchange in gray matter
Olesen, J. L., Østergaard, L., Shemesh, N., & Jespersen, S. N. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.118976 · Cited by 125
Issues in separable identification of continuous-time models with time-delay
Chen, F., Zhuan, X., Garnier, H., & Gilson, M. (2018) · Automatica · doi:10.1016/j.automatica.2018.04.014 · Cited by 26
Exploiting the Separable Structure of SLAM
Khosoussi, K., Huang, S., & Dissanayake, G. (2015) · Robotics: Science and Systems XI · doi:10.15607/rss.2015.xi.023 · Cited by 14
Metadata
- Authors
- Golub, G., & Pereyra, V.
- Venue
- Inverse Problems
- Publisher
- IOP Publishing
- Published
- 2003-02-14
- Volume
- 19
- Issue
- 2
- Pages
- R1-R26
- ISSN
- 0266-5611 (ISSN-L)
- 1361-6420
- OpenAlex
- W2090636411
- Cited by
- 760
- References
- 49
- FWCI
- 24.69
- Type
- journal article
- Language
- en
- Open access
- hybrid
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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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