References
- Bartholomew-Biggs , M. C. 1998 . Using forward accumulation for automatic differentiation of implicitly-defined functions . Comput. Optim. Appl , 9 : 65 – 84 .
- Bonett , D. G. 2006 . Comments, conjectures and conclusions: A new algorithm for the tetrachoric correlation . J. Statist. Comput. Simul , 76 ( 8 ) : 737 – 740 .
- Christianson , B. 1994 . Reverse accumulation and attractive fixed points . Optim. Methods Softw , 3 : 311 – 326 .
- Christianson , B. 1998 . Reverse accumulation and implicit functions . Optim. Methods Softw , 9 : 307 – 322 .
- Conte , S. D. and de Boor , C. 1981 . Elementary Numerical Analysis – An Algorithmic Approach , 3 , Singapore : McGraw-Hill .
- Cudeck , R. 2005 . Fitting psychometric models with methods based on automatic differentiation . Psychometrika , 70 ( 4 ) : 599 – 617 .
- Dickinson , R. P. and Gelinas , R. J. 1976 . Sensitivity analysis of ordinary differential equation systems – direct method . J. Comput. Phys , 21 ( 2 ) : 123 – 143 .
- Eberhard , P. and Bischof , C. 1999 . Automatic differentiation of numerical integration algorithms . Math. Comput , 68 ( 226 ) : 717 – 731 .
- Forth , S. A. 2006 . An efficient overloaded implementation of forward mode automatic differentiation in MATLAB . ACM Trans. Math. Softw , 32 ( 2 ) : 195 – 222 .
- Griewank , A. and Walther , A. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation , 2 Number 105 in Other Titles in Applied Mathematics, SIAM, Philadelphia, PA, 2008
- Griewank , A. , Bischof , C. , Corliss , G. , Carle , A. and Williamson , K. 1993 . Derivative convergence for iterative equation solvers . Optim. Methods Softw , 2 : 321 – 355 .
- Maly , T. and Petzold , L. R. 1996 . Numerical methods and software for sensitivity analysis of differential-algebraic systems . Appl. Numer. Math , 20 ( 1–2 ) : 57 – 79 .
- Menshikova , M. Uncertainty estimation using the moments method facilitated by automatic differentiation in Matlab Ph.D. thesis, Defence College of Management and Technology, Cranfield University, 2010
- Mohammadi , B. and Pironneau , O. 2001 . Applied Shape Optimization for Fluids , Oxford , , UK : Numerical Mathematics and Scientific Computation, Oxford University Press .
- Ortega , J. M. and Rheinboldt , W. C. 1966 . On discretization and differentiation of operators with application to Newton's method . SIAM J. Numer. Anal , 3 ( 1 ) : 143 – 156 .
- Phillips , G. M. and Taylor , P. J. 1998 . Theory and Applications of Numerical Analysis , 2 , London : Elsevier Academic Press .
- Sandu , A. 2008 . “ Reverse automatic differentiation of linear multistep methods ” . In Advances in Automatic Differentiation , Edited by: Bischof , C. H. , Martin Bücker , H. , Hovland , P. D. , Naumann , U. and Utke , J. 1 – 12 . Berlin/Heidelberg : Springer .
- Shampine , L. F. , Gladwell , I. and Brankin , R. W. 1991 . Reliable solution of special event location problems for odes . ACM Trans. Math. Softw , 17 ( 1 ) : 11 – 15 .
- Simpson , R. J.S. and Pearson , K. 1904 . Report on certain enteric fever inoculation statistics . British Medical Journal , : 1243 – 1246 .