Volume 6, Issue 4
A Memoryless Augmented Gauss-Newton Method for Nonlinear Least-Squares Problems

J. E. Dennis, Jr, Song-bai Sheng & Anh Vu Phuong

J. Comp. Math., 6 (1988), pp. 355-374

Published online: 1988-06

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  • Abstract

In this paper, we develop, analyze, and test a new algorithm for nonlinear least-squares problems. The algorithm uses a BFGS update of the Gauss-Newton Hessian when some heuristics indicate that the Gauss-Newton method may not make a good step. Some important elements are that the secant or quasi-Newton equations considered are not the obvious ones, and the method does not build up a Hessian approximation over several steps. The algorithm can be implemented easily as a modification of any Gauss-Newton code, and it seems to be useful for large residual problems.

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@Article{JCM-6-355, author = { J. E. Dennis, Jr, Song-bai Sheng and Anh Vu Phuong}, title = {A Memoryless Augmented Gauss-Newton Method for Nonlinear Least-Squares Problems}, journal = {Journal of Computational Mathematics}, year = {1988}, volume = {6}, number = {4}, pages = {355--374}, abstract = { In this paper, we develop, analyze, and test a new algorithm for nonlinear least-squares problems. The algorithm uses a BFGS update of the Gauss-Newton Hessian when some heuristics indicate that the Gauss-Newton method may not make a good step. Some important elements are that the secant or quasi-Newton equations considered are not the obvious ones, and the method does not build up a Hessian approximation over several steps. The algorithm can be implemented easily as a modification of any Gauss-Newton code, and it seems to be useful for large residual problems. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9524.html} }
TY - JOUR T1 - A Memoryless Augmented Gauss-Newton Method for Nonlinear Least-Squares Problems AU - J. E. Dennis, Jr, Song-bai Sheng & Anh Vu Phuong JO - Journal of Computational Mathematics VL - 4 SP - 355 EP - 374 PY - 1988 DA - 1988/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9524.html KW - AB - In this paper, we develop, analyze, and test a new algorithm for nonlinear least-squares problems. The algorithm uses a BFGS update of the Gauss-Newton Hessian when some heuristics indicate that the Gauss-Newton method may not make a good step. Some important elements are that the secant or quasi-Newton equations considered are not the obvious ones, and the method does not build up a Hessian approximation over several steps. The algorithm can be implemented easily as a modification of any Gauss-Newton code, and it seems to be useful for large residual problems.
J. E. Dennis, Jr, Song-bai Sheng & Anh Vu Phuong. (1970). A Memoryless Augmented Gauss-Newton Method for Nonlinear Least-Squares Problems. Journal of Computational Mathematics. 6 (4). 355-374. doi:
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