An Improved Tikhonov-Regularized Variable Projection Algorithm for Separable Nonlinear Least Squares

Axioms

Luyao Wang¹  Guolin Liu¹  Hua Guo¹ 

[1] College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China;

关键词: separable nonlinear least squares;    variable projection method;    Tikhonov regularization method;    L-curve method;    LM algorithm;   

DOI  :  10.3390/axioms10030196

来源: DOAJ

【 摘 要 】

In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using the variable projection method. Based on the truncated singular value decomposition method and the Tikhonov regularization method, we propose an improved Tikhonov regularization method, which neither discards small singular values, nor treats all singular value corrections. By fitting the Mackey–Glass time series in an exponential model, we compare the three regularization methods, and the numerically simulated results indicate that the improved regularization method is more effective at reducing the mean square error of the solution and increasing the accuracy of unknowns.

【 授权许可】

Unknown