A family of non-oscillatory 6-point interpolatory subdivision schemes. (English) Zbl 1373.65008
Subdivision schemes are a fundamental tool in approximation theory and its applications. They allow to generate recursively functions of various smoothness in a stable algorithms (such as analysed in detail in the cases in this paper), and sometimes the refinement process approximates well in a quickly convergent manner (uniform convergence in the present article). Their definition depends on the number of points and on the choice whether they are interpolatory or non-interpolatory. In this article, schemes with the former property are studied. The schemes considered here reproduce all cubic polynomials. Numerical tests are carried out, again to study the mentioned stability of the schemes. Sometimes, the recursive schemes give an unwelcome Gibbs phenomenon (oscillatory property); the subdivision algorithms analysed in this article are, however, non-oscillatory.
Reviewer: Martin D. Buhmann (Gießen)
MSC:
| 65D05 | Numerical interpolation |
| 41A05 | Interpolation in approximation theory |
| 41A10 | Approximation by polynomials |
Keywords:
nonlinear subdivision schemes; convergence; stability; approximation order; non-oscillatory; convergence; interpolatory; cubic polynomials; numerical testsReferences:
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