Approximation by Spline Functions with Free Nodes

In the last two decades, approximation by spline functions has become an important tool in applied mathematics, since the accuracy of the approximation depends only on local properties of the given function. As a consequence, spline functions with fixed nodes lead only to weak Haar spaces and the interpolation is governed by an interlacing property between the nodes and the points of interpolation. Nevertheless, a best approximation can be characterized in terms of alternants (with a possible degenerate length).