Construction of Hermite subdivision schemes reproducing polynomials

The aim of this study is to present a new class of quasi-interpolatory Hermite subdivision schemes of order two with tension parameters. This class extends and unifies some of well-known Hermite subdivision schemes, including the interpolatory Hermite schemes. Acting on a function and the associated first derivative values, each scheme in this class reproduces polynomials up to a certain degree depending on the size of stencil. This is desirable property since the reproduction of polynomials up to degree d leads to the approximation order d+1. The smoothness analysis has been performed by using the factorization framework of subdivision operators. Lastly, we present some numerical examples to demonstrate the performance of the proposed Hermite schemes.