Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

On the remainder in quadrature rules


Author: P. D. Tuan
Journal: Math. Comp. 25 (1971), 819-826
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1971-0298949-6
MathSciNet review: 0298949
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An expression is obtained for the remainder in quadrature rules applied to functions whose Hubert transforms exist. The estimation of the remainder is illustrated by means of a particular example.


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

  • [1] G. Szegö, Orthogonal Polynomials, 2nd rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1959. MR 21 #5029. MR 0106295 (21:5029)
  • [2] W. Barrett, ``Convergence properties of Gaussian quadrature formulae,'' Comput. J., v. 3, 1960/61, pp. 272-277. MR 23 #B1117. MR 0128073 (23:B1117)
  • [3] W. Barrett, ``On the convergence of Cotes' quadrature formulae,'' J. London Math. Soc., v. 39, 1964, pp. 296-302. MR 32 #3272. MR 0185812 (32:3272)
  • [4] I. D. Donaldson & D. Elliott, Quadrature I: A Unified Approach to the Development of Quadrature Rules, Math. Dept. Technical Report #23, University of Tasmania, 1970.
  • [5] J. S. Donaldson & D. Elliott, Quadrature II: The Estimation of Remainders in Certain Quadrature Rules, Math. Dept. Technical Report #24, University of Tasmania, 1970.
  • [6] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1937.
  • [7] F. G. Tricomi, Integral Equations, Interscience, New York, 1957. MR 20 #1177. MR 0094665 (20:1177)
  • [8] D. Elliott, Uniform Asymptotic Expansions of the Classical Orthogonal Polynomials and some Associated Functions, Math. Dept. Technical Report #21, University of Tasmania, 1970.
  • [9] L. J. Slater, Confluent Hypergeometric Functions, Cambridge Univ. Press, New York, 1960. MR 21 #5753. MR 0107026 (21:5753)
  • [10] A. Erdélyi, et al., Tables of Integral Transforms, vol. 2, McGraw-Hill, New York, 1954. MR 16, 468.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D30

Retrieve articles in all journals with MSC: 65D30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0298949-6
Keywords: Remainder, quadrature rules, Hilbert transform, Cauchy principal value, contour integral
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society