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Fitting uncertain data with NURBS. (English) Zbl 0938.65024

Le Méhauté, Alain (ed.) et al., Curves and surfaces with applications in CAGD. Vol. 1 of the proceedings of the 3rd international conference on Curves and surfaces, held in Chamonix-Mont-Blanc, France, June 27-July 3, 1996. Nashville, TN: Vanderbilt University Press. 177-184 (1997).
Summary: Fitting of uncertain data, that is, fitting of data points that are subject to some error, has important applications for example in statistics and for the evaluation of results from physical experiments. Fitting in these problem domains is usually achieved with polynomial approximation, which involves the minimization of an error at discrete data points. Norms typically used for this minimization include the \(l_1\), \(l_2\) and \(l_\infty\) norms, which are chosen depending on the problem domain and the expected type of error on the data points.
In this paper we describe how the \(l_1\) and \(l_\infty\) norms can be applied to integral and rational B-spline fitting as a linear programming problem. This allows for the use of B-splines and nonuniform rational B-splines (NURBS) for the fitting of uncertain data.
For the entire collection see [Zbl 0927.00038].

MSC:

65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines
65K05 Numerical mathematical programming methods
90C05 Linear programming
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