Concerning order of convergence for subdivision
The paper deals with order of \(C\)-convergence for subdivision algorithms. The usual definition of \(C\)-convergence leads to approximation properties of the so-called Schoenberg operator, subject that stability of the generators of the underlying shift invariant space assumed. However, this approach does not lead to a satisfying order result for many examples, last not least in case of interpolatory vector subdivision. Therefore, the authors try a modification of the definition of order of convergence involving an appropriate quasi-interpolant operator whose representation on polynomial spaces can be constructively determined with recourse to properties of the subdivision mask. Assuming stability and smoothness of the limit functions, the approximation order of the quasi-interpolant operator determines the order of convergence of subdivision. Several examples are also given.
scientific article; zbMATH DE number 2145928
scientific article