On the accuracy of surface spline approximation and interpolation to bump functions (Q2747917)

The author constructs a surface spline \(\sigma_h\) whose centers are vertices of the grid \(\Omega\cap h\mathbb{Z}^d\) such that \(\sigma_h\) approximates a given \(f\in C^{\gamma+ d}_0(\Omega)\) with the maximal acuracy \(O (h^{\gamma+ d})\). Here \(\gamma+ d\) is a positive even integer and the above space consists of functions with continuous derivatives of order \(\gamma+d\) and compact support \(\text{supp} \Subset \Omega\). The set \(\Omega\subset \mathbb{R}^d\) is the closure of a bounded open set.