Automatic Differentiation (AD) is a set of techniques based on the mechanical application of the chain rule to obtain derivatives of a function given as a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations such as additions or elementary functions such as exp(). By applying the chain rule of derivative calculus repeatedly to these operations, derivatives of arbitrary order can be computed automatically, and accurate to working precision. Conceptually, AD is different from symbolic differentiation and approximations by divided differences.

References in zbMATH (referenced in 12 articles )

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  1. Michael Tesch: cppduals: a nestable vectorized templated dual number library for C++11 (2019) not zbMATH
  2. Coleman, Thomas F.; Xu, Wei: Automatic differentiation in MATLAB using ADMAT with applications (2016)
  3. Haro, Àlex; Canadell, Marta; Figueras, Jordi-Lluís; Luque, Alejandro; Mondelo, Josep-Maria: The parameterization method for invariant manifolds. From rigorous results to effective computations (2016)
  4. Hascoët, Laurent; Utke, Jean: Programming language features, usage patterns, and the efficiency of generated adjoint code (2016)
  5. Kasper Kristensen and Anders Nielsen and Casper Berg and Hans Skaug and Bradley Bell: TMB: Automatic Differentiation and Laplace Approximation (2016) not zbMATH
  6. Sluşanschi, Emil I.; Dumitrel, Vlad: ADiJaC -- automatic differentiation of Java classfiles (2016)
  7. Fike, Jeffrey A.; Alonso, Juan J.: Automatic differentiation through the use of hyper-dual numbers for second derivatives (2012)
  8. Gay, David M.: Using expression graphs in optimization algorithms (2012)
  9. Reid, Peter; Gamboa, Ruben: Automatic differentiation in ACL2 (2011)
  10. Utke, Jean; Naumann, Uwe; Fagan, Mike; Tallent, Nathan; Strout, Michelle Mills; Heimbach, Patrick; Hill, Chris; Wunsch, Carl: OpenAD/F: A modular open-source tool for automatic differentiation of Fortran codes. (2008)
  11. Hart, A.; von Hippel, G. M.; Horgan, R. R.; Storoni, L. C.: Automatically generating Feynman rules for improved lattice field theories (2005)
  12. Joe, Harry; Mahbub-ul Latif, A. H. M.: Computations for the familial analysis of binary traits (2005)