An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares. (10th November 2021)

• Record Type: Journal Article
• Authors: Wang, Jiayan; Guo, Lanlan; Li, Zongmin; Wang, Xueqin; Fu, Zhengqing
• Other Names: Finocchiaro Carmelo Antonio Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-11-10
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/7625175
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : 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.