Multivariate polynomial interpolation on Lissajous-Chebyshev nodes

被引：8
作者：
Dencker, Peter [1 ]
Erb, Wolfgang [2 ]
机构：
[1] Univ Lubeck, Inst Math, Lubeck, Germany
[2] Univ Hawaii Manoa, Dept Math, Honolulu, HI 96822 USA
来源：
JOURNAL OF APPROXIMATION THEORY | 2017年 / 219卷
关键词：
Multivariate polynomial interpolation; Multivariate Lissajous curves; Lissajous-Chebyshev node points; Quadrature rules; BIVARIATE LAGRANGE INTERPOLATION; PADUA POINTS; IDEAL THEORY; VARIABLES; HYPERINTERPOLATION;
D O I：
10.1016/j.jat.2017.03.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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-Gau beta-Lobatto points in dimension one and the Padua points in dimension two. (C) 2017 Elsevier Inc. All rights reserved.
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收藏
页码：15 / 45
页数：31
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