Interval Arithmetic and Automatic Differentiation on GPU Using OpenCL

  • Grzegorz Kozikowski
  • Bartłomiej Jacek Kubica
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7782)


This paper investigates efficient and powerful approach to the Gradient and the Hessian evaluation for complex functions. The idea is to apply the parallel GPU architecture and the Automatic Differentiation methods. In order to achieve better accuracy, the interval arithmetic is used. Considerations are based on sequential and parallel authors’ implementation. In this solution, both the AD methods: Forward and Reverse modes are employed. Computational experiments include analysis of performance and are studied on the generated test functions with a given complexity.


interval computations automatic differentiation GPGPU OpenCL 


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  1. 1.
    C-XSC interval library,
  2. 2.
  3. 3.
  4. 4.
    Bücker, M.: Automatic Differentiation: Applications, Theory and Implementation. Springer (1981)Google Scholar
  5. 5.
    Collange, S., Florez, J., Defour, D.: A GPU interval library based on Boost interval (2008)Google Scholar
  6. 6.
    Hansen, E., Walster, W.: Global Optimization Using Interval Analysis. Marcel Dekker, New York (2004)zbMATHGoogle Scholar
  7. 7.
    Jastrzebski, K., Szczap, L.: Different parallelism approaches to interval computations. Master’s thesis, Faculty of Electronics and Information Technology, WUT (2009)Google Scholar
  8. 8.
    Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht (1996)zbMATHCrossRefGoogle Scholar
  9. 9.
    Kearfott, R.B., Nakao, M.T., Neumaier, A., Rump, S.M., Shary, S.P., van Hentenryck, P.:Standardized notation in interval analysis (2002)
  10. 10.
    Kamran, K., Neil, G., Firas, H.: A Performance Comparision of CUDA and OpenCL (2011),
  11. 11.
    Kozikowski, G.: Implementation of automatic differentiation library using the OpenCL technology. BEng thesis, Faculty of Electronics and Information Technology, WUT (2011)Google Scholar
  12. 12.
    Werbos, P.: Backpropagation Through Time: What It Does and How to Do ItGoogle Scholar
  13. 13.
    Kubica, B.J.: A class of problems that can be solved using interval algorithms. SCAN 2010 Proceedings. Computing 94(2-4), 271–280 (2012)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Grzegorz Kozikowski
    • 1
  • Bartłomiej Jacek Kubica
    • 1
  1. 1.Institute of Control and Computation EngineeringWarsaw University of TechnologyPoland

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