961
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Coarse grain automatic differentiation: A practical approach to fast and exact computation of first and second order derivatives in software

& | (Reviewing Editor)
Article: 1412234 | Received 24 Jun 2017, Accepted 24 Nov 2017, Published online: 27 Dec 2017

References

  • Bauer, F. L. (1974). Computational graphs and rounding error. SIAM Journal on Numerical Analysis, 11(1), 87–96.
  • Bischof, C. H., & Haghighat, M. R. (1996). Hierarchical approaches to automatic differentiation. Computational Differentiation: Techniques, Applications, and Tools, 83–94.
  • Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1--2), 167–179.
  • Duché, H. O., & Galilée, F. (2017). Second order differentiation formula in a computational graph. Retrieved from https://ssrn.com/abstract=2905103
  • Dijkstra, E. W. (1982). On the role of scientific thought. Selected writings on computing: a personal perspective. Springer. (pp. 60–66).
  • Evans, E. (2004). Domain-driven design: Tackling complexity in the heart of software. Boston, MA: Addison-Wesley Professional.
  • Francesco Faà di Bruno. (1885). Sullo sviluppo delle funzioni. Annali di scienze matematiche e fisiche, 6, 479.
  • Fowler, M. (2002). Patterns of enterprise application architecture. Boston, MA: Addison-Wesley Longman Publishing.
  • Gamma, E., Helm, R., Johnson, R., & Vlissides, J. (1995). Design patterns: Elements of reusable object-oriented software. Inc, Boston, MA: Addison-Wesley Longman Publishing.
  • Gendler, D., Naumann, U., & Christianson, B. (2007). Automatic differentiation of assembler code. Proceedings of the IADIS International Conference on Applied Computing, 431–436.
  • Giles, M., & Glasserman, P. (2006). Smoking adjoints: Fast monte carlo greeks. Risk, 19(1), 88–92.
  • Griewank, A., & Walther, A. (2008). Evaluating derivatives: Principles and techniques of algorithmic differentiation. ( Number 105 in Other Titles in Applied Mathematics, 2nd ed.). Philadelphia, PA: SIAM.
  • Henrard, M. (2011). Adjoint algorithmic differentiation: Calibration and implicit function theorem. OpenGamma Quantitative Research, (1).
  • Henrard, M. (2011). Algorithmic differentiation in finance explained. Cham: Springer.
  • Kaplan, W. (1952). Advanced calculus. Addison-Wesley mathematical series. Boston, MA: Addison-Wesley Press.
  • Martin, R. C. (2008). Clean code: A handbook of agile software craftsmanship. Pearson Education
  • Naumann, U. (2012). The art of differentiating computer programs: An introduction to algorithmic differentiation. Number 24 in Software, Environments, and Tools. Philadelphia, PA: SIAM.
  • Sutter, H. (2005). Exceptional C++ style: 40 new engineering puzzles, programming problems, and solutions. Boston, MA: Addison-Wesley.