A higher order method for solving nonlinear least-squares problems

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Persistent URL	http://purl.org/net/epubs/work/36041926
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Record Id	36041926
Title	A higher order method for solving nonlinear least-squares problems
Contributors	NIM Gould (STFC Rutherford Appleton Lab.), T Rees (STFC Rutherford Appleton Lab.), JA Scott (STFC Rutherford Appleton Lab.)
Abstract	We consider the solution of nonlinear least-squares problems. Such problems have traditionally been solved using a Gauss-Newton or Newton approximation, which is in turn globalized by either solving within a trust region, or by solving a regularized problem. We describe a hybrid method that combines these two approaches. While Newton's method uses second derivative information, we argue that, due to the sum-of-squares nature of the problem, a method we call the tensor-Newton approximation makes better use of this information. We show how the subproblem here can be solved using standard nonlinear least-squares techniques, e.g., our hybrid Gauss-Newton/Newton solver. We describe each of these methods, and give numerical results from our nonlinear least-squares solver RALFit, comparing the proposed solver with the commonly used implementation in the GNU Scientific Library.
Organisation	STFC , SCI-COMP
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Preprint	RAL Preprints RAL-P-2017-010, SIAM J Sci Comput STFC, 2017.		RAL-P-2017-010.pdf	2017