2018/01/10 by Martin Neuenhofen, Neuenhofen, Martin
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #Mathematical Software (cs.MS) #Mathematical and Theoretical Analysis #cs.MS
paper · pdf · doi:10.48550/arxiv.1801.03614
9 pages
openalex publication_date 2018/01/11 · arxiv created 2018/01/14 · arxiv updated 2018/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.