Numerische Mathematik

, Volume 115, Issue 2, pp 289–307 | Cite as

A fast numerical algorithm for the integration of rational functions

  • Dante V. Manna
  • Luis A. Medina
  • Victor H. Moll
  • Armin Straub


A new iterative method for high-precision numerical integration of rational functions on the real line is presented. The algorithm transforms the rational integrand into a new rational function preserving the integral on the line. The coefficients of the new function are explicit polynomials in the original ones. These transformations depend on the degree of the input and the desired order of the method. Both parameters are arbitrary. The formulas can be precomputed. Iteration yields an approximation of the desired integral with mth order convergence. Examples illustrating the automatic generation of these formulas and the numerical behaviour of this method are given.

Mathematics Subject Classification (2000)

Primary 65D30 Secondary 33F05 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Dante V. Manna
    • 1
  • Luis A. Medina
    • 2
    • 3
  • Victor H. Moll
    • 4
  • Armin Straub
    • 4
  1. 1.Department of Mathematics and Computer ScienceVirginia Wesleyan CollegeNorfolkUSA
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA
  3. 3.Department of MathematicsUniversidad de Puerto RicoSan JuanUSA
  4. 4.Department of MathematicsTulane UniversityNew OrleansUSA

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