On the convergence rates of Legendre approximation
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- by Haiyong Wang and Shuhuang Xiang PDF
- Math. Comp. 81 (2012), 861-877 Request permission
Abstract:
The problem of the rate of convergence of Legendre approximation is considered. We first establish the decay rates of the coefficients in the Legendre series expansion and then derive error bounds of the truncated Legendre series in the uniform norm. In addition, we consider Legendre approximation with interpolation. In particular, we are interested in the barycentric Lagrange formula at the Gauss-Legendre points. Explicit barycentric weights, in terms of Gauss-Legendre points and corresponding quadrature weights, are presented that allow a fast evaluation of the Legendre interpolation formula. Error estimates for Legendre interpolation polynomials are also given.References
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Additional Information
- Haiyong Wang
- Affiliation: Department of Applied Mathematics and Software, Central South University, Changsha, Hunan 410083, People’s Republic of China
- Address at time of publication: Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium
- Email: haiyong.wang@cs.kuleuven.be
- Shuhuang Xiang
- Affiliation: Department of Applied Mathematics and Software, Central South University, Changsha, Hunan 410083, People’s Republic of China
- Email: xiangsh@mail.csu.edu.cn
- Received by editor(s): May 7, 2010
- Received by editor(s) in revised form: February 17, 2011
- Published electronically: October 18, 2011
- Additional Notes: This work was supported by the NSF of China (No. 11071260).
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 861-877
- MSC (2010): Primary 65D05, 65D99, 41A25
- DOI: https://doi.org/10.1090/S0025-5718-2011-02549-4
- MathSciNet review: 2869040