Higher Order Automatic Differentiation with Dual Numbers

Authors

  • László Szirmay-Kalos ORCID
    Affiliation

    Department of Control Engineering and Information Technology, Faculty of Electrical Engineering and Informatics, Budapest University of Technology and Economics, H-1521 Budapest, P. O. B. 91, Hungary

https://doi.org/10.3311/PPee.16341

Abstract

In engineering applications, we often need the derivatives of functions defined by a program. The approach chosen for derivative computation must be algebraic to allow computer implementation. A particular solution to obtain first derivatives is the application of dual numbers. This paper proposes simple and compact generalizations of this idea to obtain derivatives of arbitrary order for single or multi-variate functions and the automatic handling of 0/0 ambiguities in the calculations. We also provide the C++ code that takes advantage of operator overloading and recursion. The method is demonstrated by path animation, Gaussian curvature computation, and curve fairing.

Keywords:

dual numbers, higher order automatic differentiation

Published Online

2020-10-26

How to Cite

Szirmay-Kalos, L. “Higher Order Automatic Differentiation with Dual Numbers”, Periodica Polytechnica Electrical Engineering and Computer Science, 65(1), pp. 1–10, 2021. https://doi.org/10.3311/PPee.16341

Issue

Section

Articles