Numerische Mathematik

, Volume 116, Issue 3, pp 463–491

Error bounds for approximation in Chebyshev points

Article

DOI: 10.1007/s00211-010-0309-4

Cite this article as:
Xiang, S., Chen, X. & Wang, H. Numer. Math. (2010) 116: 463. doi:10.1007/s00211-010-0309-4

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.

Mathematics Subject Classification (2000)

65D32 65D30 

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Applied Mathematics and SoftwareCentral South UniversityChangsha, HunanPeople’s Republic of China
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityKowloonHong Kong

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