Approximation Properties of Chebyshev Polynomials in the Legendre Norm

Cuixia Niu, Huiqing Liao, Heping Ma and Hua Wu
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Cuixia Niu: Department of Mathematics, Shanghai University, Shanghai 200444, China
Huiqing Liao: Department of Mathematics, Shanghai University, Shanghai 200444, China
Heping Ma: Department of Mathematics, Shanghai University, Shanghai 200444, China
Hua Wu: Department of Mathematics, Shanghai University, Shanghai 200444, China

Mathematics, 2021, vol. 9, issue 24, 1-10

Abstract: 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.

Keywords: Chebyshev polynomials; Chebyshev interpolation operator; the Legendre norm; Legendre–Chebyshev spectral method; Clenshaw–Curtis quadrature; multidomain; multi-dimensions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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