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 Chebyshev–Gauß–Lobatto points in dimension one and the Padua points in dimension two.

Multivariate polynomial interpolation on Lissajous–Chebyshev nodes

Erb W.
2017

Abstract

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 Chebyshev–Gauß–Lobatto points in dimension one and the Padua points in dimension two.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11577/3368994
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