The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering and 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 the possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular, it demonstrates ...
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The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering and 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 the possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular, it demonstrates 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.
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