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- W2766034532 abstract "The goal of this article is to provide a general multivariate framework that synthesizes well-known non-tensorial polnomial interpolation schemes on the Padua points, the Morrow-Patterson-Xu points and the Lissajous node points into a single unified theory. The interpolation nodes of these schemes are special cases of the general Lissajous-Chebyshev points studied in this article. We will characterize these Lissajous-Chebyshev points in terms of Lissajous curves and Chebyshev varieties and derive a general discrete orthogonality structure related to these points. This discrete orthogonality is used as the key for the proof of the uniqueness of the polynomial interpolation and the derivation of a quadrature rule on these node sets. Finally, we give an efficient scheme to compute the polynomial interpolants." @default.
- W2766034532 created "2017-11-10" @default.
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- W2766034532 date "2017-11-01" @default.
- W2766034532 modified "2023-09-27" @default.
- W2766034532 title "A unifying theory for multivariate polynomial interpolation on general Lissajous-Chebyshev nodes" @default.
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