Multivariate polynomial interpolation on Lissajous–Chebyshev nodes
| Autor: | Peter Dencker, Wolfgang Erb |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Multivariate Lissajous curves
Numerical Analysis Multivariate statistics Chebyshev polynomials Multivariate polynomial interpolation Lissajous–Chebyshev node points Quadrature rules Applied Mathematics General Mathematics 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Chebyshev filter Quadrature (mathematics) Polynomial interpolation Lissajous curve Applied mathematics Padua points 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Approximation Theory. 219:15-45 |
| ISSN: | 0021-9045 |
| Popis: | In this article, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets related to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes linked to these curves, we derive a discrete orthogonality structure on these node sets. Using this orthogonality structure, we obtain unique polynomial interpolation in appropriately defined spaces of multivariate Chebyshev polynomials. Our results generalize corresponding interpolation and quadrature results for the ChebyshevGauLobatto points in dimension one and the Padua points in dimension two. |
| Databáze: | OpenAIRE |
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