Bayesian Automatic Adaptive Quadrature: An Overview

  • Gheorghe Adam
  • Sanda Adam
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)


The progress obtained within the Bayesian approach to the automatic adaptive quadrature is reviewed. It is shown that the derivation of reliable Bayesian inferences, both as it concerns the construction of the subrange binary tree with its associated priority queue and the a priori validation of the input to the local quadrature rules, can be done provided the well-conditioning criteria for the integrand profile check are implemented taking into account the hardware and software environments at hand.


automatic adaptive quadrature Bayesian inference local quadrature rule integrand profile well-conditioning criteria subrange binary tree 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adam, G.: Case studies in the numerical solution of oscillatory integrals. Rom. Journ. Phys. 38, 527–538 (1993)zbMATHGoogle Scholar
  2. 2.
    Adam, G., Adam, S.: The Boundary Layer Problem in Bayesian Adaptive Quadrature. Physics of Particles and Nuclei Letters 5(3), 269–273 (2008)CrossRefGoogle Scholar
  3. 3.
    Adam, G., Adam, S.: Principles of the Bayesian automatic adaptive quadrature. Numerical Methods and Programming: Advanced Computing 10, 391–397 (2009), Google Scholar
  4. 4.
    Adam, G., Adam, S.: Floating point degree of precision of an interpolatory quadrature sum. Rom. Journ. Phys. 55, 469–479 (2010)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Adam, G., Adam, S., Plakida, N.M.: Reliability conditions on quadrature algorithms. Comp. Phys. Comm. 154(1), 49–64 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Adam, G., Adam, S., Ţifrea, A., Neacşu, A.: Resolving thin boundary layers in numerical quadrature. Romanian Reports in Physics 58(4), 155–166 (2006)Google Scholar
  7. 7.
    Adam, G., Nobile, A.: Product integration rules at Clenshaw-Curtis and related points: a robust implementation. IMA J. Numerical Analysis 11, 271–296 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Adam, S., Adam, G.: Floating Point Degree of Precision in Numerical Quadrature. In: Adam, G., Buša, J., Hnatič, M. (eds.) MMCP 2011. LNCS, vol. 7125, pp. 189–194. Springer, Heidelberg (2012)Google Scholar
  9. 9.
    Clenshaw, C.W., Curtis, A.R.: A method for numerical integration on an automatic computer. Num. Math. 2, 197–205 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration, 2nd edn. Academic Press, Orlando (1984)zbMATHGoogle Scholar
  11. 11.
    Goldberg, D.: What Every Computer Scientist Should Know about Floating-Point Arithmetic. Computing Surv. (March 1991),
  12. 12.
    Kahan, W.: How Futile are Mindless Assessments of Roundoff in Floating-Point Computation (2006),
  13. 13.
    Krommer, A.R., Ueberhuber, C.W.: Computational Integration. SIAM, Philadelphia (1998)CrossRefzbMATHGoogle Scholar
  14. 14.
    Lyness, J.N.: When not to use an automatic quadrature routine. SIAM Rev. 25, 63–87 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
  16. 16.
    Piessens, R., de Doncker-Kapenga, E., Überhuber, C.W., Kahaner, D.K.: QUADPACK, a subroutine package for automatic integration. Springer, Berlin (1983)zbMATHGoogle Scholar
  17. 17.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in Fortran 77 – The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gheorghe Adam
    • 1
    • 2
  • Sanda Adam
    • 1
    • 2
  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia
  2. 2.Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH)MagureleRomania

Personalised recommendations