A Memoryless Augmented Gauss-Newton Method for Nonlinear Least-Squares Problems | Zendy

J. E. Dennis | Zendy; J. E. Songbai | Zendy; Vu Sheng | Zendy; An Tran Hung Phuong | Zendy

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A Memoryless Augmented Gauss-Newton Method for Nonlinear Least-Squares Problems

Author(s) -

J. E. Dennis,

J. E. Songbai,

Vu Sheng,

An Tran Hung Phuong

Publication year - 1985

Publication title -

rice digital scholarship archive (rice university)

Language(s) - English

Resource type - Reports

DOI - 10.21236/ada454936

Subject(s) - hessian matrix , quasi newton method , broyden–fletcher–goldfarb–shanno algorithm , gauss , non linear least squares , residual , newton's method , mathematics , least squares function approximation , nonlinear system , algorithm , mathematical optimization , computer science , estimation theory , physics , statistics , quantum mechanics , computer network , asynchronous communication , estimator

: 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 hueristics 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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