Approximation Properties of Chebyshev Polynomials in the Legendre Norm

被引：2
|
作者：
Niu, Cuixia [1 ,2 ]
Liao, Huiqing [1 ]
Ma, Heping [1 ]
Wu, Hua [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Shandong Technol & Business Univ, Sch Comp Sci & Technol, Yantai 264000, Peoples R China
来源：
MATHEMATICS | 2021年 / 9卷 / 24期
关键词：
Chebyshev polynomials; Chebyshev interpolation operator; the Legendre norm; Legendre-Chebyshev spectral method; Clenshaw-Curtis quadrature; multidomain; multi-dimensions; SPECTRAL VISCOSITY METHOD;
D O I：
10.3390/math9243271
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we present some important approximation properties of Chebyshev polynomials in the Legendre norm. We mainly discuss the Chebyshev interpolation operator at the Chebyshev-Gauss-Lobatto points. The cases of single domain and multidomain for both one dimension and multi-dimensions are considered, respectively. The approximation results in Legendre norm rather than in the Chebyshev weighted norm are given, which play a fundamental role in numerical analysis of the Legendre-Chebyshev spectral method. These results are also useful in Clenshaw-Curtis quadrature which is based on sampling the integrand at Chebyshev points.
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页数：10
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