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 

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.

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References

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    Lanczos, C.: Introduction to: Tables of Chebyshev Polynomials. (Applied Math. Series, Vol. 9.) Washington: National Bureau of Standards 1952.Google Scholar
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    Clenshaw, C. W., Curtis, A. R.: A method for Numerical Integration on an Automatic Computer. Numer. Math.2, 197–205 (1960).Google Scholar
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    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
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    Davis, P. J.: Interpolation and Approximation. New York: Blaisdell 1963.Google Scholar
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    Riess, R. D., Johnson, L. W.: Error Estimates for Clenshaw-Curtis Quadrature. Numer. Math.18, 345–353 (1972).Google Scholar
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    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

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