Abstract
Lagrange interpolation by finite-dimensional spaces of multivariate spline functions defined on a polyhedral regionK in ℝk is studied. A condition of Schoenberg-Whitney type is introduced. The main result of this paper shows that this condition characterizes all configurationsT inK such that in every neighborhood ofT inK there must exist a configuration\(\tilde T\) which admits unique Lagrange interpolation.
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Communicated by M. Gasca
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Sommer, M., Strauss, H. A condition of Schoenberg-Whitney type for multivariate spline interpolation. Adv Comput Math 5, 381–397 (1996). https://doi.org/10.1007/BF02124752
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DOI: https://doi.org/10.1007/BF02124752