Abstract
We consider results regarding Bernstein and Cheney–Sharma-type operators that interpolate functions defined on triangles with straight and curved sides and we introduce a new Cheney–Sharma-type operator for the triangle with one curved side, highlighting the symmetry between the methods. We present some properties of the operators, their products and Boolean sums and some results regarding the remainders of the corresponding approximation formulas, using modulus of continuity and Peano’s theorem. Additionally, we consider some numerical examples to show the approximation properties of the given operators.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference40 articles.
1. Smooth interpolation in triangles
2. Polynomial interpolation to boundary data on triangles
3. Bernstein-type operators on triangle;Blaga;Rev. Anal. Numer. Theor. Approx.,2009
4. Blending interpolation schemes on triangle with error bounds;Böhmer;Lect. Notes Math.,1977
5. Some interpolation operators on a simplex domain;Cătinaş;Stud. Univ. Babeş–Bolyai Math.,2007