The Art of Differentiating Computer Programs

This is the first entry-level book on algorithmic (also known as automatic) differentiation (AD), providing fundamental rules for the generation of first- and higher-order tangent-linear and adjoint code. The author covers the mathematical underpinnings as well as applications to real-world numerical simulation programs. Readers will find: • Many examples and exercises, including hints to solutions • The prototype AD tools dco and dcc for use with the examples and exercises • First- and higher-order tangent-linear and adjoint modes for a limited subset of C/C++, provided by the derivative code compiler dcc • A supplementary website containing sources of all software discussed in the book, additional exercises and comments on their solutions (growing over the coming years), links to other sites on AD, and errata. Ideal for undergraduate and graduate students, the book is also suitable for researchers and developers at all levels who need an introduction to AD.

Uwe Naumann is Associate Professor for Computer Science at RWTH Aachen University. He has co-chaired international conferences on AD held in Nice (2000), Chicago (2004) and Bonn (2008) and co-edited the proceedings for those conferences. His professional interests are primarily motivated by AD. They range from compilers for the semantic transformation of numerical programs via corresponding (domain-specific) program analyses and combinatorial algorithms to high-performance scientific computing and the application of adjoint methods in computational science, engineering and finance. He has co-authored more than 80 publications and is a member of SIAM and of the Numerical Algorithms Group, Ltd.