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On the Gaussian integration of Chebyshev polynomials


Authors: A. R. Curtis and P. Rabinowitz
Journal: Math. Comp. 26 (1972), 207-211
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1972-0298934-5
MathSciNet review: 0298934
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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$.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0298934-5
Keywords: Gaussian integration, Chebyshev polynomials of the first kind, asymptotic error, numerical integration error
Article copyright: © Copyright 1972 American Mathematical Society