Open Mathematics (Aug 2021)

Construction of a family of non-stationary combined ternary subdivision schemes reproducing exponential polynomials

  • Zhang Zeze,
  • Zheng Hongchan,
  • Pan Lulu

DOI
https://doi.org/10.1515/math-2021-0058
Journal volume & issue
Vol. 19, no. 1
pp. 909 – 926

Abstract

Read online

In this paper, we propose a family of non-stationary combined ternary (2m+3)\left(2m+3)-point subdivision schemes, which possesses the property of generating/reproducing high-order exponential polynomials. This scheme is obtained by adding variable parameters on the generalized ternary subdivision scheme of order 4. For such a scheme, we investigate its support and exponential polynomial generation/reproduction and get that it can generate/reproduce certain exponential polynomials with suitable choices of the parameters and reach 2m+32m+3 approximation order. Moreover, we discuss its smoothness and show that it can produce C2m+2{C}^{2m+2} limit curves. Several numerical examples are given to show the performance of the schemes.

Keywords