Approximation by local \(\mathbb L\)-splines that are exact on subspaces of the kernel of a differential operator (Q643845)

The authors present a construction of local \(\mathcal L\)-splines. They consider a linear differential operator \(\mathcal L_r\) of order \(r\) with constant real coefficients and real pairwise distinct roots of the characteristic polynomial and they give a local \(\mathcal L\)-spline with uniform knots, which is exact an all functions from the subspaces \(\ker \mathcal{L}_m\), \(m\leq r\). In the second theorem an estimation for the approximation error is given.