Advertisement

BIT Numerical Mathematics

, Volume 17, Issue 1, pp 31–38 | Cite as

Convergence of osculatory quadrature formulae

  • John D. Donaldson
Article
  • 15 Downloads

Abstract

The regions of analyticity of functions to be integrated using equally spaced osculatory quadrature formulae are obtained. As a by-product it is noted that the asymptotic forms used are applicable to estimating or placing bounds on errors.

Keywords

Computational Mathematic Quadrature Formula Asymptotic Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Pólya, Über die Konvergenz von Quadraturverfahren, Math. Zeit., 37 (1933), 264–286.Google Scholar
  2. 2.
    W. Barrett,Convergence Properties of Gaussian Quadrature Formulae, Comp. J. 3 (1960), 272–277.Google Scholar
  3. 3.
    W. Barrett,On the Convergence of Cotes Quadrature Formulae, J. Lond. Math. Soc., 39 (1964), 296–302.Google Scholar
  4. 4.
    P.J. Davis,On a Problem in the Theory of Mechanical Quadratures, Pac. J. of Math., 5 (1955), 669–674.Google Scholar
  5. 5.
    M. M. Chawla,Convergence of Newton-Cotes Quadratures for Analytic Functions, BIT 11 (1971), 159–167.Google Scholar
  6. 6.
    V. I. Krylov,Approximate Calculation of Integrals, MacMillan Co., New York (1962).Google Scholar
  7. 7.
    J. D. Donaldson and D. Elliott,A Unified Approach to Quadrature Rules with Asymptotic Estimates of the Remainder Term, SIAM J. of Num. Anal., 9 (1972), p. 573–602.Google Scholar
  8. 8.
    J. D. Donaldson,Estimates of Upper Bounds for Quadrature Errors, SIAM J. of Num. Anal., 10 (1973), p. 13–22.Google Scholar
  9. 9.
    M. M. Chawla and M. K. Jain,Asymptotic Error Estimates for the Gauss Quadrature Formulae, Math. of Comp. 22 (1968), 91–97.Google Scholar
  10. 10.
    J. D. Donaldson and D. Elliott,Quadrature II: The Estimation of Remainders in Certain Quadrature Rules, Univ. of Tas. Tech. Report No. 24.Google Scholar
  11. 11.
    N. G. De Bruijn,Asymptotic Methods in Analysis, North Holland (1958).Google Scholar
  12. 12.
    V. I. Krylov and L. T. Sulgina,On the Convergence of a Quadrature Process, Dokl. Akad. Nauk USSR 6 (1962), 139–141, MR 25 # 3607.Google Scholar

Copyright information

© BIT Foundations 1977

Authors and Affiliations

  • John D. Donaldson
    • 1
  1. 1.Department of MathematicsThe University of TasmaniaHobartAustralia

Personalised recommendations