The concern here is with Gauss-type quadrature rules that are exact for a mixture of polynomials and rational functions, the latter being selected so as to simulate poles that may be present in the integrand. The underlying theory is presented as well as methods for constructing such rational Gauss formulae. Relevant computer routines are provided and applied to a number of examples, including Fermi-Dirac and Bose-Einstein integrals of interest in solid state physics. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 30 articles , 1 standard article )

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  1. Deeb, Ahmad; Hamdouni, A.; Razafindralandy, Dina: Comparison between Borel-Padé summation and factorial series, as time integration methods (2016)
  2. Berriochoa Esnaola, E.; Cachafeiro López, A.; Cala Rodríguez, F.; Illán González, J.; Rebollido Lorenzo, J.M.: Gauss rules associated with nearly singular weights (2015)
  3. Deckers, Karl; Bultheel, Adhemar: The existence and construction of rational Gauss-type quadrature rules (2012)
  4. Fritzsche, Bernd; Kirstein, Bernd; Lasarow, Andreas: Para-orthogonal rational matrix-valued functions on the unit circle (2012)
  5. Berriochoa Esnaola, Elías; Cachafeiro López, Alicia; Illán-González, J. R.; Martínez-Brey, E.: Chebyshev series method for computing weighted quadrature formulas (2011)
  6. Deckers, K.; Bultheel, A.; Van Deun, J.: A generalized eigenvalue problem for quasi-orthogonal rational functions (2011)
  7. Bultheel, Adhemar; Cruz-Barroso, Ruymán; Deckers, Karl; González-Vera, Pablo: Rational Szegő quadratures associated with Chebyshev weight functions (2009)
  8. Illán González, J.R.: Gaussian rational quadrature formulas for ill-scaled integrands (2009)
  9. López Lagomasino, G.; Reichel, L.; Wunderlich, L.: Matrices, moments, and rational quadrature (2008)
  10. de la Calle Ysern, B.; González-Vera, P.: Rational quadrature formulae on the unit circle with arbitrary poles (2007)
  11. Fasino, Dario; Gemignani, Luca: Structured eigenvalue problems for rational Gauss quadrature (2007)
  12. Fidalgo Prieto, U.; Illán González, J.R.; López Lagomasino, G.: Convergence and computation of simultaneous rational quadrature formulas (2007)
  13. Zhang, Shangyou: Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements (2007)
  14. Darius, L.; González-Vera, P.; Jiménez Paiz, M.: Quadrature formulas associated with rational modifications of the Chebyshev weight functions (2006)
  15. de la Calle Ysern, Bernardo: Error bounds for rational quadrature formulae of analytic functions (2005)
  16. Gautschi, Walter: The Hardy-Littlewood function: an exercise in slowly convergent series (2005)
  17. Bultheel, A.; González-Vera, P.; Hendriksen, E.; Njåstad, Olav: Orthogonal rational functions and quadrature on the real half line. (2003)
  18. Bultheel, A.; González-Vera, P.; Hendriksen, E.; Njåstad, Olav: Quadrature and orthogonal rational functions (2001)
  19. Gautschi, Walter: The use of rational functions in numerical quadrature (2001)
  20. Laurie, Dirk P.: Computation of Gauss-type quadrature formulas (2001)

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