The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.If the standard deviation a is known Wahba suggests minimizing T(P) = F(P) - ( 5.51) while other authors suggest (see Wahba 1990) that p should be determined as the root of F(p) = ma2 , (5.52) or even better as the root of F(p) = a2Tr(I - K(p)) .
|Title||:||Curve and Surface Fitting with Splines|
|Publisher||:||Oxford University Press - 1995|