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BIT Numerical Mathematics

, Volume 13, Issue 2, pp 145–152 | Cite as

Optimal rules for numerical integration round the unit circle

  • M. M. Chawla
  • Veena Kaul
Article

Abstract

The construction of optimal linear rules of numerical approximation by Davis' method has already been discussed for functions analytic in circles and in certain ellipses. In the present paper, introducing an appropriate Hilbert space, we discuss optimal linear rules for functions analytic in a circular annulus. We then consider the construction of optimal rules for numerical integration round the unit circleC1 : ∣z∣=1. In Theorem 2 we obtain explicitly a family of optimal rules forεc1f(z)∣dz∣, withf analytic onC1; interestingly, in general, the optimal nodes do not lie onC1. For functionsf(1/2(z +z−1)), Theorem 2 gives a family of optimal quadrature formulas for integration over [−1,1].

Keywords

Hilbert Space Computational Mathematic Unit Circle Numerical Approximation 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.

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References

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    P. J. Davis, Errors of Numerical Approximation for Analytic Functions, J. Rational Mech. Anal. 2 (1953), 303–313.Google Scholar
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    P. J. Davis, Interpolation and Approximation, Blaisdell, New York, 1963.Google Scholar

Copyright information

© BIT Foundations 1973

Authors and Affiliations

  • M. M. Chawla
    • 1
  • Veena Kaul
    • 1
  1. 1.Department of MathematicsIndian Institute of TechnologyNew Delhi-29India

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