Abstract
The multivariate interpolating (m, l, s)-splines are a natural generalization of Duchon's thin plate splines (TPS). More precisely, we consider the problem of interpolation with respect to some finite number of linear continuous functionals defined on a semi-Hilbert space and minimizing its semi-norm. The (m, l, s)-splines are explicitly given as a linear combination of translates of radial basis functions. We prove the existence and uniqueness of the interpolating (m, l, s)-splines and investigate some of their properties. Finally, we present some practical examples of (m, l, s)-splines for Lagrange and Hermite interpolation.
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Bouhamidi, A., Le Méhauté, A. Multivariate interpolating (m, l, s)-splines. Advances in Computational Mathematics 11, 287–314 (1999). https://doi.org/10.1023/A:1018940429434
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DOI: https://doi.org/10.1023/A:1018940429434