Splines and estimation of nonlinear parameters. (English) Zbl 0677.41014

Girard, D.; Laurent, P. J.

Mathematical methods in computer aided geometric design, Pap. Int. Conf., Oslo/Norw. 1988, 273-298 (1989).

Summary: [For the entire collection see Zbl 0669.00011.]
Given the approximate values \(z_ i\) at points \(t_ 1,...,t_ n\) of a function f having some particular features (determined by \(\alpha)\), the purpose is to smooth the data and simultaneously to estimate \(\alpha\). For example, \(\alpha\) might be the location of peaks or discontinuities, the value of a period, etc. The idea is to use the smoothing spline corresponding to a well chosen quadratic smoothness criterion \(L_{\alpha}\). Such a criterion can be built using the inf-convolution of several quadratic functionals. Characterizations and computational methods for the resulting splines are presented here. In addition, we discuss the use of the generalized cross-validation method for choosing both the smoothing parameter and \(\alpha\). Several algorithms are given and the efficiency is illustrated on several types of numerical examples.

MSC:

41A15

Spline approximation

Keywords:

computational methods; algorithms; numerical examples

Citations:

Zbl 0669.00011