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

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

Zbl 0669.00011