3 years ago

Review of theory and implementation of hyper-dual numbers for first and second order automatic differentiation.

Martin Neuenhofen

In this review we present hyper-dual numbers as a tool for the automatic differentiation of computer programs via operator overloading.

We start with a motivational introduction into the ideas of algorithmic differentiation. Then we illuminate the concepts behind operator overloading and dual numbers.

Afterwards, we present hyper-dual numbers (and vectors) as an extension of dual numbers for the computation of the Jacobian and the Hessian matrices of a computer program. We review a mathematical theorem that proves the correctness of the derivative information that is obtained from hyper-dual numbers.

Finally, we refer to a freely available implementation of a hyper-dual number class in Matlab. We explain an interface that can be called with a function as argument such that the Jacobian and Hessian of this function are returned.

Publisher URL: http://arxiv.org/abs/1801.03614

DOI: arXiv:1801.03614v2

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