The art of differentiating computer programs. An introduction to algorithmic differentiation. 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 how to apply these observations to real-world numerical simulation programs.par 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.par Audience: This book is intended for undergraduate and graduate students in computational science, engineering, and finance as well as applied mathematics and computer science. It will provide researchers and developers at all levels with an intuitive introduction to AD.

References in zbMATH (referenced in 32 articles , 1 standard article )

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  1. Alger, Nick; Chen, Peng; Ghattas, Omar: Tensor train construction from tensor actions, with application to compression of large high order derivative tensors (2020)
  2. Andersson, Joel A. E.; Gillis, Joris; Horn, Greg; Rawlings, James B.; Diehl, Moritz: CasADi: a software framework for nonlinear optimization and optimal control (2019)
  3. Khan, Kamil A.: Whitney differentiability of optimal-value functions for bound-constrained convex programming problems (2019)
  4. Maddison, James R.; Goldberg, Daniel N.; Goddard, Benjamin D.: Automated calculation of higher order partial differential equation constrained derivative information (2019)
  5. Balakin, D. A.: Numerical methods for computing plausibility and belief distributions of consequences of a subjective model of object of research (2018)
  6. Barton, Paul I.; Khan, Kamil A.; Stechlinski, Peter; Watson, Harry A. J.: Computationally relevant generalized derivatives: theory, evaluation and applications (2018)
  7. Breden, Maxime; Lessard, Jean-Philippe: Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs (2018)
  8. Griewank, Andreas; Hasenfelder, Richard; Radons, Manuel; Lehmann, Lutz; Streubel, Tom: Integrating Lipschitzian dynamical systems using piecewise algorithmic differentiation (2018)
  9. Hück, Alexander; Bischof, Christian; Sagebaum, Max; Gauger, Nicolas R.; Jurgelucks, Benjamin; Larour, Eric; Perez, Gilberto: A usability case study of algorithmic differentiation tools on the ISSM ice sheet model (2018)
  10. Khan, Kamil A.: Branch-locking AD techniques for nonsmooth composite functions and nonsmooth implicit functions (2018)
  11. Kusch, Lisa; Albring, T.; Walther, A.; Gauger, N. R.: A one-shot optimization framework with additional equality constraints applied to multi-objective aerodynamic shape optimization (2018)
  12. Pryce, John D.; Nedialkov, Nedialko S.; Tan, Guangning; Li, Xiao: How AD can help solve differential-algebraic equations (2018)
  13. Römer, Ulrich; Narayanamurthi, Mahesh; Sandu, Adrian: Solving parameter estimation problems with discrete adjoint exponential integrators (2018)
  14. Sagebaum, Max; Albring, T.; Gauger, N. R.: Expression templates for primal value taping in the reverse mode of algorithmic differentiation (2018)
  15. Towara, M.; Naumann, U.: SIMPLE adjoint message passing (2018)
  16. Wang, Mu; Lin, Guang; Pothen, Alex: Using automatic differentiation for compressive sensing in uncertainty quantification (2018)
  17. Beinker, Mark; Schlenkrich, Sebastian: Accurate vega calculation for Bermudan swaptions (2017)
  18. Charpentier, Isabelle: Optimized higher-order automatic differentiation for the Faddeeva function (2016)
  19. Evtushenko, Yu. G.; Zubov, V. I.: Generalized fast automatic differentiation technique (2016)
  20. Gower, R. M.; Gower, A. L.: Higher-order reverse automatic differentiation with emphasis on the third-order (2016)

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