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Comparison of three newton-like nonlinear least-squares methods for estimating parameters of ground-water flow models

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Abstract

Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.

Additional Publication Details

Publication type:
Conference Paper
Publication Subtype:
Conference Paper
Title:
Comparison of three newton-like nonlinear least-squares methods for estimating parameters of ground-water flow models
Volume
1
Year Published:
1992
Language:
English
Publisher:
Publ by Computational Mechanics Publ
Publisher location:
Southampton, United Kingdom
Larger Work Title:
Finite Elements in Water Resources, Proceedings of the International Conference
First page:
379
Last page:
386
Number of Pages:
8
Conference Title:
Proceedings of the 9th International Conference on Computational Methods in Water Resources
Conference Location:
Denver, CO, USA
Conference Date:
1 June 1992 through 1 June 1992