Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Nonlinear curve-fitting in the $ L\sb{1}$ and $ L\sb{\infty }$ norms


Authors: Richard L. Shrager and Edward Hill
Journal: Math. Comp. 34 (1980), 529-541
MSC: Primary 41A45; Secondary 41A50, 65D10
MathSciNet review: 559201
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 41A45, 41A50, 65D10

Retrieve articles in all journals with MSC: 41A45, 41A50, 65D10


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0559201-X
PII: S 0025-5718(1980)0559201-X
Article copyright: © Copyright 1980 American Mathematical Society