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Error bounds for approximation in Chebyshev points

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Abstract

This paper improves error bounds for Gauss, Clenshaw–Curtis and Fejér’s first quadrature by using new error estimates for polynomial interpolation in Chebyshev points. We also derive convergence rates of Chebyshev interpolation polynomials of the first and second kind for numerical evaluation of highly oscillatory integrals. Preliminary numerical results show that the improved error bounds are reasonably sharp.

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Authors and Affiliations

  1. Department of Applied Mathematics and Software, Central South University, Changsha, Hunan, 410083, People’s Republic of China

    Shuhuang Xiang & Haiyong Wang

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

    Xiaojun Chen

Authors
  1. Shuhuang Xiang
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  2. Xiaojun Chen
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  3. Haiyong Wang
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Corresponding author

Correspondence to Shuhuang Xiang.

Additional information

This paper is supported partly by NSF of China (No.10771218) and the Program for New Century Excellent Talents in University, State Education Ministry, China.

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Xiang, S., Chen, X. & Wang, H. Error bounds for approximation in Chebyshev points. Numer. Math. 116, 463–491 (2010). https://doi.org/10.1007/s00211-010-0309-4

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  • DOI: https://doi.org/10.1007/s00211-010-0309-4

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