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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Autores principales:	Jiayan Wang, Lanlan Guo, Zongmin Li, Xueqin Wang, Zhengqing Fu
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/58a480ee03124b70b800323b7d0e3bef
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spelling	oai:doaj.org-article:58a480ee03124b70b800323b7d0e3bef2021-11-22T01:09:58ZAn Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares2314-478510.1155/2021/7625175https://doaj.org/article/58a480ee03124b70b800323b7d0e3bef2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/7625175https://doaj.org/toc/2314-4785For 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.Jiayan WangLanlan GuoZongmin LiXueqin WangZhengqing FuHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Jiayan Wang Lanlan Guo Zongmin Li Xueqin Wang Zhengqing Fu An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares
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
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
title	An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares
title_short	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_sort	efficient algorithm for ill-conditioned separable nonlinear least squares
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/58a480ee03124b70b800323b7d0e3bef
work_keys_str_mv	AT jiayanwang anefficientalgorithmforillconditionedseparablenonlinearleastsquares AT lanlanguo anefficientalgorithmforillconditionedseparablenonlinearleastsquares AT zongminli anefficientalgorithmforillconditionedseparablenonlinearleastsquares AT xueqinwang anefficientalgorithmforillconditionedseparablenonlinearleastsquares AT zhengqingfu anefficientalgorithmforillconditionedseparablenonlinearleastsquares AT jiayanwang efficientalgorithmforillconditionedseparablenonlinearleastsquares AT lanlanguo efficientalgorithmforillconditionedseparablenonlinearleastsquares AT zongminli efficientalgorithmforillconditionedseparablenonlinearleastsquares AT xueqinwang efficientalgorithmforillconditionedseparablenonlinearleastsquares AT zhengqingfu efficientalgorithmforillconditionedseparablenonlinearleastsquares
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An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares

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