Automatic Differentiation of Third Order Derivatives using Forward Mode in C++

Abstract

Automatic differentiation of third order derivatives is implemented in C++. The implementation uses uses object-orientation and operator overloading to perform the differentiation. A short introduction to operator overloading is done with complex numbers. Automatic differentiation of univariate functions is then extended to the second and third derivatives of multivariate function. A set of functions for benchmarking is given, and numerical results which describe the cost of calculating the derivatives are presented.