Differentiation via Logarithmic Expansions

Michael C. Fu (), Bernd Heidergott, Haralambie Leahu () and Felisa J. Vázquez-Abad
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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

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 01, 1-13

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.

Keywords: Finite difference algorithm; numerical differentiation; Taylor series expansions; sensitivity analysis; directional derivative (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595919500349

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