Abstract
Lagrange interpolation by finite-dimensional spaces of multivariate spline functions defined on a polyhedral regionK in ℝ k 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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