Model adjointization and its cost

Science in China, Series F: Information Sciences

Volumn 47, Issue 5, 2004, Pages 587-611

  Cheng, Qiang ^a,b   Zhang, Linbo ^a   Wang, Bin ^b  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

^b INSTITUTE OF ATMOSPHERIC PHYSICS   (China)

Author keywords

Automatic differentiation; Floating point operations; Least program behavior; Model adjointization

Indexed keywords

EID: 24644479217     PISSN: 10092757     EISSN: None     Source Type: Journal    
DOI: 10.1360/02yf0440     Document Type: Article

References (20)

1. Bartholomew-Biggs, M. C., Brown, S., Christianson, B. et al., Automatic differentiation of algorithms, Journal of Computational and Applied Mathematics, 2000, 124: 171-190.
2. Le Dimet, F. X., Talagrand, O., Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus, 1986, 38(A): 97-110.
3. Mu M., Nonlinear singular vectors and nonlinear singular values. Science in China, Ser. D, 2000, 43: 375-385.
4. Cacui, D. G., Sensitivity theory for nonlinear systems, II: Extension to additional classes of responses, Journal of Mathematical Physics, 1981, 22(12): 2803-2812.
5. Bischof, C., Pusch, G., Knoesel, R., Sensitivity analysis of the MM5 weather model using automatic differentiation. Computers in Physics, 1996, 0: 605-612.
6. Griewank, A., On Automatic Differentiation, Mathematical Programming: Recent Developments and Applications (eds. Iri, M.), Amsterdam: Kluwer Academic Publishers, 1989, 83-108.
7. Volin, Y. M., Ostrovskill, G. M., Automatic computation of derivatives with the use of the multi-class differentiation techniques, Computers and Mathematics with Applications, 1985, 11: 1099-1114.
8. Griewank, A., An implementation of checkpointing for the reverse or adjoint model of differentiation, ACM Trans. Math. Software, 1999, 26(1): 1-19.
9. Griewank, A., Achieve logarithmic growth of temporal and spatial complexity in reverse automatic differentiation, Optimization Methods and Software, 1992, 1: 35-54.
10. Bischof, C., Carle, A., Khademi, P. et al., Automatic Differentiation: Obtaining Fast and Reliable Derivatives - Fast in Control Problems in Industry (eds. Lasiecka, I., Morton, B.), Birkhauser, Boston: CRPC version, 1995, 1-6.
11. Rostating, N., Dalmas, S., Galligo, A., Automatic differentiation in Odyssee, Tellus, 1993, 45(A): 558-568.
12. Giering, R., Kaminski, T., Recipes for adjoint code construction, ACM Trans, on Math. Software, 1998, 24(4): 437-474.
13. Griewank, A., Some Bounds on the Complexity of Gradients, Jacobians, and Hessians, Complexity in Nonlinear Optimization (ed. Pardalos, P. M.), River Edge, NJ: World Scientific Publishers, 1993, 128-161.
14. Linnainmaa, S., Taylor expansion of the accumulated rounding error, BIT, 1976, 16: 146-160.
15. Griewank, A., Evaluating derivatives: Principles and techniques of automatic differen-Tiation, Series Frontiers in Appl. Math. SIAM, 2000, 19: 15-36.
16. Wengert, R. E., A simple automatic derivative evaluation program, Comm. ACM, 1964, 7(8): 463-464.
17. Gilbert, J. C., Automatic differentiation and iterative processes, Optimization and Software, 1992, 1(1): 13-22.
18. Griewank, A., Bischof, C., Corliss, G. et al., Derivative convergence of iterative equation solvers, Optimization Methods and Software, 1993, 2: 321-355.
19. Hovland, P., Bischof, C., Spiegelman, D., Efficient derivative codes through automatic differenti-Bation and interface contraction: An application in biostatistics, SIAM, 1997, 18(4): 1056-1066.
20. Wolfe, Checking the calculation of gradients, ACM Trans. Math. Software, 1982, 6(4): 337-343.