CALCOLO

, Volume 32, Issue 1–2, pp 39–50 | Cite as

New symmetric interpolatory quadrature formulas

  • P. Favati
  • G. Lotti
  • F. Romani
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Abstract

We introduce two families of symmetric, interpolatory integration formulas on the interval [−1,1]. These formulas, related to the class of recursive monotone stable (RMS) formulas, allow the application of higher order or compound rules with an efficient reuse of computed function values. One family (SM) uses function values computed outside the integration interval, the other one (HR) uses derivative data. These formulas are evaluated using a practical test based on a tecnique for comparing automatic quadrature routine introduced by Lyness and Kaganove and improved by the authors.

Keywords

Integration Interval Practical Test Roundoff Error Derivative Data Integrand Function 
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

  1. [1]
    P. Davis, P. Rabinowitz,Methods of Numerical Integration, (1984) Academic Press, New York.MATHGoogle Scholar
  2. [2]
    P. Favati, G. Lotti, F. Romani,Testing Automatic Quadrature Programs, Calcolo 27 (1990), 169–193.CrossRefMathSciNetGoogle Scholar
  3. [3]
    P. Favati, G. Lotti, F. Romani,Interpolatory Integration Formulas for Optimal Composition, ACM Trans. Math. Software 17 (1991), 207–21.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    P. Favati, G. Lotti, F. Romani,Asymptotic Expansion of Error in Interpolatory Quadrature, Comput. Math. Appl. 24 (1992), 99–104.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    P. Favati, G. Lotti, F. Romani,Theoretical and Practical Efficiency Measures for Symmetric Interpolatory Quadrature Formulas, BIT 34 (1994), 546–557.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    J. N. Lyness, J. J. Kaganove,A technique for comparing automatic quadrature routines, Comput. J. 20 (1977), 170–177.CrossRefGoogle Scholar
  7. [7]
    R. Piessens, E. De Doncker-Kapenga, C. Überhuber, D. K. Kahaner,QUADPACK: A Subroutine Package for Automatic Integration, (1983) Springer, Berlin.MATHGoogle Scholar
  8. [8]
    H. Sugiura andT. Sakurai,On the construction of High-Order Integration Formulae for the adaptive quadrature method, J. Comput. Appl. Math. 28 (1989), 367–381.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Instituto di Elaborazione della Informazione del CNR 1996

Authors and Affiliations

  • P. Favati
    • 1
  • G. Lotti
    • 2
  • F. Romani
    • 3
  1. 1.PisaItaly
  2. 2.Dipartimento di MatematicaUniversity of ParmaParmaItaly
  3. 3.Dipartimento di InformaticaUniversity of PisaPisaItaly

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