An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares
For separable nonlinear least squares models, a variable projection algorithm based on matrix factorization is studied, and the ill-conditioning of the model parameters is considered in the specific solution process of the model. When the linear parameters are estimated, the Tikhonov regularization...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7625175 |
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| _version_ | 1832565380469489664 |
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| author | Jiayan Wang Lanlan Guo Zongmin Li Xueqin Wang Zhengqing Fu |
| author_facet | Jiayan Wang Lanlan Guo Zongmin Li Xueqin Wang Zhengqing Fu |
| author_sort | Jiayan Wang |
| collection | DOAJ |
| description | For separable nonlinear least squares models, a variable projection algorithm based on matrix factorization is studied, and the ill-conditioning of the model parameters is considered in the specific solution process of the model. When the linear parameters are estimated, the Tikhonov regularization method is used to solve the ill-conditioned problems. When the nonlinear parameters are estimated, the QR decomposition, Gram–Schmidt orthogonalization decomposition, and SVD are applied in the Jacobian matrix. These methods are then compared with the method in which the variables are not separated. Numerical experiments are performed using RBF neural network data, and the experimental results are analyzed in terms of both qualitative and quantitative indicators. The results show that the proposed algorithms are effective and robust. |
| format | Article |
| id | doaj-art-58a480ee03124b70b800323b7d0e3bef |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-58a480ee03124b70b800323b7d0e3bef2025-02-03T01:07:58ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/7625175An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least SquaresJiayan Wang0Lanlan Guo1Zongmin Li2Xueqin Wang3Zhengqing Fu4University of Petroleum (Huadong)Shandong University of Science and TechnologyUniversity of Petroleum (Huadong)Shandong University of Science and TechnologyShandong University of Science and TechnologyFor separable nonlinear least squares models, a variable projection algorithm based on matrix factorization is studied, and the ill-conditioning of the model parameters is considered in the specific solution process of the model. When the linear parameters are estimated, the Tikhonov regularization method is used to solve the ill-conditioned problems. When the nonlinear parameters are estimated, the QR decomposition, Gram–Schmidt orthogonalization decomposition, and SVD are applied in the Jacobian matrix. These methods are then compared with the method in which the variables are not separated. Numerical experiments are performed using RBF neural network data, and the experimental results are analyzed in terms of both qualitative and quantitative indicators. The results show that the proposed algorithms are effective and robust.http://dx.doi.org/10.1155/2021/7625175 |
| spellingShingle | Jiayan Wang Lanlan Guo Zongmin Li Xueqin Wang Zhengqing Fu An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares Journal of Mathematics |
| title | An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares |
| title_full | An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares |
| title_fullStr | An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares |
| title_full_unstemmed | An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares |
| title_short | An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares |
| title_sort | efficient algorithm for ill conditioned separable nonlinear least squares |
| url | http://dx.doi.org/10.1155/2021/7625175 |
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