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.

引用

页数：10

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