Advertisement

Computing

, Volume 15, Issue 4, pp 347–355 | Cite as

Quadrature formulas for cauchy principal value integrals

  • M. M. Chawla
  • N. Jayarajan
Article

Abstract

Quadrature formulas of the Clenshaw-Curtis type, based on the “practical” abscissasxk=cos(kπ/n),k=0(1)n, are obtained for the numerical evaluation of Cauchy principal value integrals\(\int\limits_{ - 1}^1 {(x - a)^{ - 1} } f(x) dx, - 1< a< 1\).

Keywords

Computational Mathematic Numerical Evaluation Quadrature Formula 
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.

Quadraturformeln für Cauchysche Hauptwertintegrale

Zusammenfassung

Die Quadraturformeln vom Clenshaw-Curtis Typ, die auf den “praktischen” Abszissenxk=cos(kπ/n),k=0(1)n, basieren, werden für die numerische Berechnung des Cauchyschen Hauptwerts\(\int\limits_{ - 1}^1 {(x - a)^{ - 1} } f(x) dx, - 1< a< 1\), abgeleitet.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Lanczos, C.: Introduction to: Tables of Chebyshev Polynomials. (Applied Math. Series, Vol. 9.) Washington: National Bureau of Standards 1952.Google Scholar
  2. [2]
    Clenshaw, C. W., Curtis, A. R.: A method for Numerical Integration on an Automatic Computer. Numer. Math.2, 197–205 (1960).Google Scholar
  3. [3]
    Paget, D. F., Elliott, D.: An Algorithm for the Numerical Evaluation of Certain Cauchy Principal Value Integrals. Numer. Math.19, 373–385 (1972).Google Scholar
  4. [4]
    Davis, P. J.: Interpolation and Approximation. New York: Blaisdell 1963.Google Scholar
  5. [5]
    Riess, R. D., Johnson, L. W.: Error Estimates for Clenshaw-Curtis Quadrature. Numer. Math.18, 345–353 (1972).Google Scholar
  6. [6]
    Chawla, M. M.: Error Estimates for the Clenshaw-Curtis Quadrature. Math. Comp.22, 651–656 (1968).Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • M. M. Chawla
    • 1
  • N. Jayarajan
    • 1
  1. 1.Department of MathematicsIndian Institute of TechnologyNew Delhi-29India

Personalised recommendations