Abstract
The mathematical theory underlying the practical method of “surface spline interpolation” provides approximation theory with an intrinsic concept of multivariate spline ready for use. A proper abstract setting is shown to be some Hilbert function space, the reproducing kernel of which involves no functions more complicated than logarithms. The crux of the matter is that convenient representation forpiulas can be obtained by resorting to convolutions or to Fourier transforms of distributions.
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© 1979 Springer Science+Business Media Dordrecht
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Meinguet, J. (1979). An Intrinsic Approach to Multivariate Spline Interpolation at Arbitrary Points. In: Sahney, B.N. (eds) Polynomial and Spline Approximation. NATO Advanced Study Institutes Series, vol 49. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9443-0_12
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DOI: https://doi.org/10.1007/978-94-009-9443-0_12
Publisher Name: Springer, Dordrecht
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