Fitting simple non-tensor-product splines to scattered noisy data on Euclidean d-space

摘要

A family of formally simple non-tensor-product splines has already proven useful for estimating smooth real-valued functions on Rd from their given noisy values at finitely many ‘spots’. These splines are uniquely defined by the values they take at the ‘knots’. Choosing the knot set different from the given data spot set is a useful option (e.g., when spot design is poor, or for reasons of data reduction). Spline determination is described for this general case, together with statistical estimation of the proper degree of smoothing. Test results are presented, and use in pragmatic systems modelling and simulation is sketched.