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Nonlinear Curve-Fitting in the $L_1$ and $L_\infty$ Norms

Richard I. Shrager and Edward Hill, Jr.
Mathematics of Computation
Vol. 34, No. 150 (Apr., 1980), pp. 529-541
DOI: 10.2307/2006101
Stable URL: http://www.jstor.org/stable/2006101
Page Count: 13
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Nonlinear Curve-Fitting in the $L_1$ and $L_\infty$ Norms
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Abstract

In extending the Levenberg-Marquardt $L_2$ method for nonlinear curve-fitting to the $L_1$ and $L_\infty$ norms, the following problems arise, but are dealt with successfully: (1) Trial parameters are generated by linear programming, which can be time-consuming. (2) Trial parameters are not uniquely specified in some cases. (3) There are intervals of the search parameter for which the trial parameters remain constant. (4) In $L_1$, the trial parameters are discontinuous with respect to the search parameter. It is shown that linear constraints on the parameters are easily included in the computations. Finally, some numerical results are presented.

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