Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the Gaussian integration of Chebyshev polynomials

Authors: A. R. Curtis and P. Rabinowitz
Journal: Math. Comp. 26 (1972), 207-211
MSC: Primary 65D30
MathSciNet review: 0298934
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that as $m$ tends to infinity, the error in the integration of the Chebyshev polynomial of the first kind, ${T_{(4m + 2)j \pm 2l}}(x)$, by an $m$-point Gauss integration rule approaches ${( - 1)^j} \cdot 2/(4{l^2} - 1),l = 0,1, \cdots ,m - 1$, and ${( - 1)^j} \cdot \pi /2,l = m$, for all $j$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D30

Retrieve articles in all journals with MSC: 65D30

Additional Information

Keywords: Gaussian integration, Chebyshev polynomials of the first kind, asymptotic error, numerical integration error
Article copyright: © Copyright 1972 American Mathematical Society