Surface tiffing and smoothing splines techniques are widely used in practice to fit data arising from many different application areas such as meteorology, insurance and stock exchange. A common problem is the approximation of functios of many variables for given values of the function at various points What makes the problem even more complicated is that the given or observed values may contain nise. We are particularly intereasted in data mining applications which deal with very large databases. These problems arise in many diffeerent areas [4]. One basic aim in data miing is to model functional relationships of high dimensional data sets which in-troduce the "curse of dimensionality". In order to overcome this curse, additive and interaction splines have been used [9]. Generalised additive models, if interaction terms are limited to order two interactions. lead to the determination of coupled surfaces and curves. Thus, an important part of any data analysis algorithm for these problems is the determination of an approximating surface for extremetly large data sets.
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