Approximation Properties of Chebyshev Polynomials in the Legendre Norm

Mathematics

Hua Wu¹  Cuixia Niu¹  Huiqing Liao¹  Heping Ma¹ 

[1] Department of Mathematics, Shanghai University, Shanghai 200444, China;

关键词: Chebyshev polynomials;    Chebyshev interpolation operator;    the Legendre norm;    Legendre–Chebyshev spectral method;    Clenshaw–Curtis quadrature;    multidomain;   

DOI  :  10.3390/math9243271

来源: DOAJ

【 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.

【 授权许可】

Unknown