Affiliation:
1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an , Shaanxi 710072 , P. R. China
Abstract
Abstract
In this paper, we propose a family of non-stationary combined ternary
(
2
m
+
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
2
m
+
3
2m+3
approximation order. Moreover, we discuss its smoothness and show that it can produce
C
2
m
+
2
{C}^{2m+2}
limit curves. Several numerical examples are given to show the performance of the schemes.