The authors provide a new ternary 4-point approximating subdivision scheme. This new scheme is based on the evaluation at some points of the interpolating Lagrange polynomials of node points
. This subdivision scheme has smoothness
, an approximation order of four and its support has size 5.5. The authors provide a table with comparisons of these characteristics with other known subdivision schemes. As pointed in the article, this idea of using values of Lagrange interpolating polynomials can be extended to ternary
-point approximation subdivision schemes, using Lagrange interpolation polynomials of higher degree.