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On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules

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  • Shuhuang Xiang
  • Guo He
  • Haiyong Wang

Abstract

Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, together with the efficient evaluation of the modified moments by forward recursions or by Oliver’s algorithms, this paper presents fast and stable interpolating integration algorithms, by using the coefficients and modified moments, for Clenshaw-Curtis, Fejér’s first- and second-type rules for Jacobi weights or Jacobi weights multiplied by a logarithmic function. Numerical examples illustrate the stability, efficiency, and accuracy of these quadratures.

Suggested Citation

  • Shuhuang Xiang & Guo He & Haiyong Wang, 2014. "On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, August.
    • Handle: RePEc:hin:jnlaaa:436164
    DOI: 10.1155/2014/436164
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    Cited by:

    1. Liu, Guidong & Xiang, Shuhuang, 2023. "An efficient quadrature rule for weakly and strongly singular integrals," Applied Mathematics and Computation, Elsevier, vol. 447(C).

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