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Mathematics of Computation

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On the error in the numerical integration of Chebyshev polynomials


Authors: D. Nicholson, P. Rabinowitz, Nira Richter-Dyn and D. Zeilberger
Journal: Math. Comp. 25 (1971), 79-86
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1971-0300443-0
MathSciNet review: 0300443
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Abstract: A general method is described to compute the exact error in the numerical integration of a given polynomial by certain types of integration rules. This method is applied to get exact errors in the integration of certain Chebyshev polynomials of the first kind by Gauss and Lobatto rule and asymptotic errors in the integration of Chebyshev polynomials of both kinds by Gauss, Lobatto and Radau rules.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0300443-0
Keywords: Numerical integration, exact error, asymptotic error, Jacobi polynomial, Chebyshev polynomial, Gauss rule, Lobatto rule, Radau rule
Article copyright: © Copyright 1971 American Mathematical Society