Abstract
For practical problems of data fitting in two dimensions two methods seem to be most popular: Thin Plate Splines (TPS) Duchon (1976) and Hardy’s Multiquadric Surfaces (MQS) Hardy (1971), (1982), see also Franke (1982). The theory for TPS has been developed in a series of papers (see Duchon (1976), Meinguet (1979)). However, beyond its numerical performance little seems to be known about MQS. For instance, in his lecture notes for a recent meeting, Franke (1983) raised (based on extensive numerical experience) the followine conjecture.
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Micchelli, C.A. (1984). Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions. In: Singh, S.P., Burry, J.W.H., Watson, B. (eds) Approximation Theory and Spline Functions. NATO ASI Series, vol 136. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6466-2_7
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DOI: https://doi.org/10.1007/978-94-009-6466-2_7
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