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Approximation Properties of Chebyshev Polynomials in the Legendre Norm

Author

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  • Cuixia Niu

    (Department of Mathematics, Shanghai University, Shanghai 200444, China
    School of Computer Science and Technology, Shandong Technology and Business University, Yantai 264000, 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)

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.

Suggested Citation

  • Cuixia Niu & Huiqing Liao & Heping Ma & Hua Wu, 2021. "Approximation Properties of Chebyshev Polynomials in the Legendre Norm," Mathematics, MDPI, vol. 9(24), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3271-:d:704386
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