Interpolation by Uni- and Multivariate Generalized Splines Original Research Article

Lagrange interpolation by finite-dimensional spaces of uni- and multivariate generalized spline functions (including polynomial splines) is studied. Using a condition of Schoenberg-Whitney type, it is shown how to change an almost interpolation set in order to obtain a set which admits unique Lagrange interpolation. Moreover, it is shown that every regular space of univariate generalized splines is a weak Chebyshev space if and only if every interpolation set can be characterized by a modified Schoenberg-Whitney type condition.