High order approximation by CCC-spline quasi-interpolants.

Inspired by CCC-Schoenberg operators that converge only quadratically, this paper proposes a generalization that has provably higher order of convergence. Two kinds of proposed approximations can be chosen to have order less or equal than the order of the underlying CCC-spline space. With the intention to compare our approximations with an interpolant, its error bound is also calculated. The proposed methods of maximal order are comparable with the interpolant and usually show more acceptable behavior. As an application of the new methods, certain boundary value problems are solved in the sense of quasi-collocation. [ABSTRACT FROM AUTHOR]