Error bounds for approximation in Chebyshev points

Shuhuang Xiang; Xiaojun Chen; Haiyong Wang

doi:10.1007/s00211-010-0309-4

Error bounds for approximation in Chebyshev points

Shuhuang Xiang, Xiaojun Chen, Haiyong Wang

Research output: Journal article publication › Journal article › Academic research › peer-review

62 Citations (Scopus)

Abstract

This paper improves error bounds forGauss, Clenshaw-Curtis and Fejér's first quadrature by using newerror estimates for polynomial interpolation inChebyshev 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.

Original language	English
Pages (from-to)	463-491
Number of pages	29
Journal	Numerische Mathematik
Volume	116
Issue number	3
DOIs	https://doi.org/10.1007/s00211-010-0309-4
Publication status	Published - 21 May 2010

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics

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10.1007/s00211-010-0309-4

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abstract = "This paper improves error bounds forGauss, Clenshaw-Curtis and Fej{\'e}r's first quadrature by using newerror estimates for polynomial interpolation inChebyshev 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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N2 - This paper improves error bounds forGauss, Clenshaw-Curtis and Fejér's first quadrature by using newerror estimates for polynomial interpolation inChebyshev 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.

AB - This paper improves error bounds forGauss, Clenshaw-Curtis and Fejér's first quadrature by using newerror estimates for polynomial interpolation inChebyshev 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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JO - Numerische Mathematik

JF - Numerische Mathematik

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Error bounds for approximation in Chebyshev points

Abstract

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