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 | 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 $j$.

- Milton Abramowitz and Irene A. Stegun,
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*Asymptotic estimates for the error of the Gauss-Legendre quadrature formula*, Comput. J.**11**(1968/69), 339–340. MR**237096**, DOI https://doi.org/10.1093/comjnl/11.3.339 - D. Nicholson, P. Rabinowitz, Nira Richter-Dyn, and D. Zeilberger,
*On the error in the numerical integration of Chebyshev polynomials*, Math. Comp.**25**(1971), 79–86. MR**300443**, DOI https://doi.org/10.1090/S0025-5718-1971-0300443-0 - Philip Rabinowitz,
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Keywords:
Gaussian integration,
Chebyshev polynomials of the first kind,
asymptotic error,
numerical integration error

Article copyright:
© Copyright 1972
American Mathematical Society