Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



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
MathSciNet review: 0300443
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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

  • Philip J. Davis and Philip Rabinowitz, Numerical integration, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0211604
  • Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D30

Retrieve articles in all journals with MSC: 65D30

Additional Information

Keywords: Numerical integration, exact error, asymptotic error, Jacobi polynomial, Chebyshev polynomial, Gauss rule, Lobatto rule, Radau rule
Article copyright: © Copyright 1971 American Mathematical Society