Error bounds for approximation in Chebyshev points

被引：75

作者：

Xiang, Shuhuang ^{[1
]}

Chen, Xiaojun ^{[2
]}

Wang, Haiyong ^{[1
]}

机构：

[1] Cent S Univ, Dept Appl Math & Software, Changsha 410083, Hunan, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

NUMERISCHE MATHEMATIK | 2010年 / 116卷 / 03期

关键词：

HIGHLY OSCILLATORY INTEGRALS; CLENSHAW-CURTIS; PRODUCT-INTEGRATION; QUADRATURE; IMPLEMENTATION; COMPUTATION; RULES;

D O I：

10.1007/s00211-010-0309-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper improves error bounds for Gauss, Clenshaw-Curtis and Fej,r'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.

引用

页码：463 / 491

页数：29

共 32 条

[1] PRODUCT INTEGRATION RULES AT CLENSHAW-CURTIS AND RELATED POINT - A ROBUST IMPLEMENTATION
ADAM, G
NOBILE, A
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 1991, 11 (02) : 271 - 296
[2] [Anonymous], 2000, SIAM
[3] [Anonymous], 1964, HDB MATH FUNCTIONS
[4] [Anonymous], 2000, TABLES INTEGRALS SER
[5] [Anonymous], 1984, Methods of Numerical Integration
[6] Bernstein S., 1912, Mem. Cl. Sci. Acad. R. Belg, V4, P1
[7] Barycentric Lagrange interpolation
Berrut, JP
Trefethen, LN
[J]. SIAM REVIEW, 2004, 46 (03) : 501 - 517
[8] Boyd JP, 2000, CHEBYSHEV FOURIER SP
[9] Dahlquist G., 2007, Numerical methods in scientific computing, VI.
[10] Complex Gaussian quadrature of oscillatory integrals
Deano, Alfredo
Huybrechs, Daan
[J]. NUMERISCHE MATHEMATIK, 2009, 112 (02) : 197 - 219

← 1 2 3 4 →