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Differentiation via Logarithmic Expansions

Author

Listed:
  • Michael C. Fu

    (Smith School of Business & Institute for Systems Research, University of Maryland, College Park, USA)

  • Bernd Heidergott

    (Department of Econometrics and Operations Research, VU Amsterdam, Netherlands)

  • Haralambie Leahu

    (Department of Mathematics, University of Amsterdam, Amsterdam, Netherlands)

  • Felisa J. Vázquez-Abad

    (Department of Computer Science, Hunter College of City University of New York, New York, USA5Computer and Information Systems, The University of Melbourne, Australia)

Abstract

In this note, we introduce a new finite difference approximation called the Black-Box Logarithmic Expansion Numerical Derivative (BLEND) algorithm, which is based on a formal logarithmic expansion of the differentiation operator. BLEND capitalizes on parallelization and provides derivative approximations of arbitrary precision, i.e., our analysis can be used to determine the number of terms in the series expansion to guarantee a specified number of decimal places of accuracy. Furthermore, in the vector setting, the complexity of the resulting directional derivative is independent of the dimension of the parameter.

Suggested Citation

  • Michael C. Fu & Bernd Heidergott & Haralambie Leahu & Felisa J. Vázquez-Abad, 2020. "Differentiation via Logarithmic Expansions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-13, January.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:01:n:s0217595919500349
    DOI: 10.1142/S0217595919500349
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    References listed on IDEAS

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    1. Nico M. Dijk, 2011. "Error Bounds and Comparison Results: The Markov Reward Approach For Queueing Networks," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 9, pages 397-459, Springer.
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