Error bounds for approximation in Chebyshev points

Authors:
Shuhuang Xiang;Xiaojun Chen;Haiyong Wang
Affiliations:
Central South University, Department of Applied Mathematics and Software, 410083, Changsha, Hunan, People’s Republic of China;The Hong Kong Polytechnic University, Department of Applied Mathematics, Kowloon, Hong Kong;Central South University, Department of Applied Mathematics and Software, 410083, Changsha, Hunan, People’s Republic of China
Venue:
Numerische Mathematik
Year:
2010

Citing 0
Cited 4

Minimizing the Condition Number of a Gram Matrix

SIAM Journal on Optimization
Efficient quadrature of highly oscillatory integrals with algebraic singularities

Journal of Computational and Applied Mathematics
Computation of integrals with oscillatory and singular integrands using Chebyshev expansions

Journal of Computational and Applied Mathematics
On graded meshes for weakly singular Volterra integral equations with oscillatory trigonometric kernels

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

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.