BibTeX
@INCOLLECTION{
Fike2012ADT,
title = "Automatic Differentiation Through the Use of HyperDual Numbers for Second
Derivatives",
doi = "10.1007/9783642300233_15",
author = "Jeffrey A. Fike and Juan J. Alonso",
abstract = "Automatic Differentiation techniques are typically derived based on the chain rule
of differentiation. Other methods can be derived based on the inherent mathematical properties of
generalized complex numbers that enable firstderivative information to be carried in the nonreal
part of the number. These methods are capable of producing effectively exact derivative values.
However, when secondderivative information is desired, generalized complex numbers are not
sufficient. Higherdimensional extensions of generalized complex numbers, with multiple nonreal
parts, can produce accurate secondderivative information provided that multiplication is
commutative. One particular number system is developed, termed hyperdual numbers, which produces
exact first and secondderivative information. The accuracy of these calculations is demonstrated
on an unstructured, parallel, unsteady ReynoldsAveraged NavierStokes solver.",
pages = "163173",
crossref = "Forth2012RAi",
booktitle = "Recent Advances in Algorithmic Differentiation",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
address = "Berlin",
volume = "87",
editor = "Shaun Forth and Paul Hovland and Eric Phipps and Jean Utke and Andrea Walther",
isbn = "9783540689355",
issn = "14397358",
year = "2012",
ad_theotech = "Hessian"
}
