A Family of Binary Univariate Nonstationary Quasi-Interpolatory Subdivision Reproducing Exponential Polynomials

In this paper, by suitably using the so-called push-back operation, a connection between the approximating and interpolatory subdivision, a new family of nonstationary subdivision schemes is presented. Each scheme of this family is a quasi-interpolatory scheme and reproduces a certain space of exponential polynomials. This new family of schemes unifies and extends quite a number of the existing interpolatory schemes reproducing exponential polynomials and noninterpolatory schemes like the cubic exponential B-spline scheme. For these new schemes, we investigate their convergence, smoothness, and accuracy and show that they can reach higher smoothness orders than the interpolatory schemes with the same reproduction property and better accuracy than the exponential B-spline schemes. Several examples are given to illustrate the performance of these new schemes.