## A ternary 4-point approximating subdivision scheme.(English)Zbl 1144.65012

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 $$-1,0,1,2$$. This subdivision scheme has smoothness $$C^2$$, 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 $$(2n+2)$$-point approximation subdivision schemes, using Lagrange interpolation polynomials of higher degree.

### MSC:

 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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### References:

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