The poisedness of interpolation problem for splines

We study the poisedness of interpolation problem for univariate spline spaces and the location of interpolation points relative to spline knots, and obtain two new complete characterizations of poisedness condition. They are equivalent to the Schoenberg-Whitney theorem, but they are very valid for poisedness test of sample points for a spline space. We present the concepts of local poised set, minimal poised set and perfect local poised set for the configuration of interpolation points with respect to spline space and obtain complete characterizations of them.