Automatic Differentiation Bibliography

compiled by George F. Corliss

This bibliography was originally published in Automatic Differentiation of Algorithms: Theory, Implementation, and Application [Grie91e] as the common bibliography for all of the papers in that volume. Each author prepared a bibliography for her or his own paper. The separate bibliographies were merged into a single BibTex database, and references from several other sources were added. Especially valuable contributions were made by bibliographic data bases previously compiled by Bruce Char, by David Gay, and by Davis, Corliss, and Krenz [Davi88a]. Additional works are added as they come to my attention.

This bibliography includes most of the work known to the editors in the area of automatic differentiation. Because it includes all of the works cited by any paper in [Grie91e], it includes many citations that are not directly related to automatic differentiation. For example, it includes basic references in optimization, symbolic algebra systems, and several applications areas.

The file all brec.bib is a standard BibTex data base. It assumes commands to get Russian digraphs:

  \newcommand{\Yu}{{Yu}}
  \newcommand{\Ye}{{Ye}}
  \newcommand{\Ju}{{Ju}}

This report is produced by the file all cite.tex.

The electronic version of this bibliography is available from netlib (netlib@research.att.com) and by anonymous ftp from boris.mscs.mu.edu (134.48.4.4) in directory pub/corliss/Autodiff. Corrections and additions are welcome and should be sent to

Dr. George F. Corliss

Department of Mathematics, Statistics,

and Computer Science Marquette University Milwaukee, WI 53233 USA georgec@boris.mscs.mu.edu

References

[Aber88a] O. Aberth, Precise Numerical Analysis, William Brown, Dubuque, Iowa, 1988.

[Abra70a] M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, Dover, New York, 1970.

[AdaLRM] Ada Joint Program Office, Reference Manual for the Ada Programming Language, ANSI/MIL–STD–1815A, Washington, D.C., 1983.

[Adam69a] D. S. Adamson and C. W. Winant, A SLANG simulation of an initially strong shock wave downstream of an infinite area change, in Proceedings of the Conference on Applications of Continuous-System Simulation Languages, 1969, pp. 231–240.

[AFNO83a] AFNOR, Le langage de programmation FORTRAN, norme ISO 1539 (norme NF Z 65-110), Association Française de Normalisation, Tour Europe, Cedex 7, F-92080 Paris La Defense Cedex, France, 1983.

[Ahoa86a] A. V. Aho, R. Sethi, and J. D. Ullman, Compilers: Principles, Techniques, and Tools, Addison-Wesley, Reading, Mass., 1986.

[Aida89a] K. R. Aida-Zade and Yu. G. Evtushenko, Bystroe avtomaticheskoe differentsirovanie na ÈVM (Fast automatic differentiation), Matematicheskoe Modelirovanie (Mathematical Modelling), 1 (1989), pp. 121–139. (In Russian).

[Alef83a] G. Alefeld and J. Herzberger, Introduction to Interval Computations, Academic Press, New York, 1983.

[Ande79a] L. Anderson and N. H. Ibragimov, Lie-Backlund Transformations in Applications, Studies in Applied Mathematics, SIAM, Philadelphia, Penn., 1979.

[Arbe86a] P. Arbenz and W. Gander, Solving nonlinear eigenvalue problems by algorithmic differentiation, Computing, 36 (1986), pp. 205–215.

[Arbi87a] M. Arbib, Brains, Machines, and Mathematics, Springer Verlag, Berlin, 1987.

[Ball69a] W. E. Ball, BSOLVE: Solution to a set of nonlinear equations by Marquardt’s method, in Material and Energy Balance Computations, E. J. Henley and E. M. Rosen, eds., John Wiley and Sons, New York, 1969, pp. 560–566.

[Ball73a] , The BSOLVE subroutine, in Optimization Techniques with FORTRAN, J. L. Kuester and J. H. Mize, eds., McGraw-Hill, New York, 1973, pp. 240–250.

[Bard74a] Y. Bard, Nonlinear Parameter Estimation, Academic Press, New York, 1974.

[Bart89a] M. C. Bartholomew-Biggs, L. C. W. Dixon, Z. Maany, and M. Mohseninia, Three papers on automatic differentiation presented at the IFAC Symposium on “Dynamic Modelling & Control of National Economies,” July 1989, Edinburgh, Scotland, Technical Report No. 223, The Numerical Optimisation Center, Hatfield Polytechnic, Hatfield, U.K., 1988. Contains Automatic Differentiation of Large Sparse Systems, Automatic Differentiation and Constrained Optimization, and Parallel Automatic Differentiation in Ada Applied to the Navier Stokes Equations.

[Bart80a] D. Barton, On Taylor series and stiff equations, ACM Trans. Math. Software, 6 (1980), pp. 280–294.

[Bart70a] D. Barton, I. M. Willers, and R. V. M. Zahar, The automatic solution of ordinary differential equations by the method of Taylor series., Computer J., 14 (1970), pp. 243–248.

[Bart71a] , Taylor series methods for ordinary differential equations – An evaluation, in Mathematical Software, J. Rice, ed., Academic Press, New York, 1971, pp. 369–390.

[Baue74a] F. L. Bauer, Computational graphs and rounding errors, SIAM J. on Numerical Analysis, 11 (1974), pp. 87–96.

[Baur83a] W. Baur and V. Strassen, The complexity of partial derivatives, Theoretical Computer Science, 22 (1983), pp. 317–330.

[Beck88a] R. A. Becker, J. M. Chambers, and A. R. Wilks, The New S Language, Computer Science Series, Wadsworth and Brooks/Cole, Pacific Grove, Calif., 1988.

[Beda59a] L. M. Beda, L. N. Korolev, N. V. Sukkikh, and T. S. Frolova, Programs for automatic differentiation for the machine BESM, Technical Report, Institute for Precise Mechanics and Computation Techniques, Academy of Science, Moscow, USSR, 1959. (In Russian).

[Bell65a] R. E. Bellman, H. H. Kagiwada, and R. E. Kalaba, Wengert’s numerical method for partial derivatives, orbit determination, and quasilinearization, Comm. ACM, 8 (1965), pp. 231–232.

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[Berz87a] M. Berz, The differential algebra FORTRAN precompiler DAFOR, Technical

Report AT–3 TN–87–32, Los Alamos National Laboratory, Los Alamos, N.M., 1987.

[Berz87b] , The method of power series tracking for the mathematical description of beam dynamics, Nuclear Instruments and Methods, A258 (1987), pp. 431 +.

[Berz88a] , Differential algebraic description and analysis of trajectories in vacuum electronic devices including spacecharge effects, IEEE Transactions on Electron Devices, 53 (1988), pp. 2002 +.

[Berz88b] , Differential algebraic treatment of beam dynamics to very high orders including applications to spacecharge, AIP Conference Proceedings, 177 (1988), pp. 275 +.

[Berz89c] , The description of particle accelerators using high order perturbation theory on maps, in Physics of Particle Accelerators, vol. 1, M. Month, ed., American Institute of Physics, 1989, pp. 961 +.

[Berz89a] , Differential algebraic description of beam dynamics to very high order, Particle Accelerators, 24 (1989), p. 109.

[Berz90e] , Arbitrary order description of arbitrary particle optical systems, Nuclear Instruments and Methods, A298 (1990), pp. 426 +.

[Berz90c] , Computational aspects of design and simulation: COSY INFINITY, Nuclear Instruments and Methods, A298 (1990), pp. 473 +.

[Berz90d] , COSY INFINITY, an arbitrary order general purpose optics code, in Computer Codes and the Linear Accelerator Community, Los Alamos LA–11857–C, 1990, pp. 137 +.

[Berz90b] , COSY INFINITY version 3 reference manual, Technical Report MSUCL – 751, National Superconducting Cyclotron Lab., Michigan State University, East Lansing, Mich., 1990.

[Berz90f] , The DA precompiler DAFOR, Technical Report, Lawrence Berkeley National Laboratory, Berkeley, Calif., 1990.

[Berz90a] , Differential algebra precompiler version 3 — Reference manual, Technical Report MSUCL – 755, National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Mich., 1990.

[Berz91b] , COSY INFINITY version 4 reference manual, Technical Report MSUCL – 771, National Superconducting Cyclotron Lab., Michigan State University, East Lansing, Mich., 1991.

[Berz91a] , Forward algorithms for high orders and many variables with application to beam physics, in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, A. Griewank and G. F. Corliss, eds., SIAM, Philadelphia, Penn., 1991, pp. 147–156.

[Berz91c] , Automatic differentiation as an application of nonarchimedean analysis, IMACS Annals of Computing and Applied Mathematics, (in print).

[Berz89b] , Differential algebra – A new tool, in Proceedings of the 1989 IEEE Particle Accelerator Conference, F. Bennet and J. Kopta, eds., IEEE, March 20–23, 1989.

[Berz87c] M. Berz and H. Wollnik, The program HAMILTON for the analytic solution of the equations of motion in particle optical systems through fifth order, Nuclear Instruments and Methods, A258 (1987), pp. 364 +.

[Bigg71a] M. C. Biggs, Minimization algorithms making use of non-quadratic properties of the objective function, J. the Institute of Mathematics and Its Applications, 8 (1971), pp. 315–327.

[Bigg73a] , A note on minimization algorithms which make use of non-quadratic properties of the objective function, J. the Institute of Mathematics and Its Applications,

12 (1973), pp. 337–338.

[Bisc91a] C. Bischof, Issues in parallel automatic differentiation, in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, A. Griewank and G. F. Corliss, eds., SIAM, Philadelphia, Penn., 1991, pp. 100–113.

[Bisc92b] C. Bischof, A. Carle, G. Corliss, and A. Griewank, ADIFOR: Automatic differentiation in a source translation environment, Preprint MCS–P288–0192, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., January 1992. ADIFOR Working Note # 5. Accepted for the International Symposium on Symbolic and Algebraic Computation, July 27–29, 1992, Berkeley, Calif.

[Bisc91j] C. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland, ADI-FOR: Fortran source translation for efficient derivatives, Preprint MCS–P278–1291, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., December 1991. ADIFOR Working Note # 4.

[Bisc91f] , Generating derivative codes from Fortran programs, Preprint MCS–P263– 0991, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., February 1992. Also appeared as Technical Report 91185, Center for Research in Parallel Computation, Rice University, Houston, Tex.

[Bisc92c] , Generating derivative codes from Fortran programs, Scientific Computing, (to appear). ADIFOR Working Note # 1. Also appeared as Preprint MCS–P263– 0991, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., September 1991, and as Technical Report 91185, Center for Research in Parallel Computation, Rice University, Houston, Tex., 1991.

[Bisc92a] C. Bischof, G. Corliss, and A. Griewank, ADIFOR exception handling, Technical Memorandum ANL/MCS–TM–159, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., January 1992. ADIFOR Working Note # 3.

[Bisc92d] , Structured second- and higher-order derivatives through univariate Taylor series, Preprint MCS–P296–0392, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., March 1992. ADIFOR Working Note # 6.

[Bisc92e] C. Bischof and M. El-Khadiri, On exploiting partial separability and extending the compile-time reverse mode in ADIFOR, Technical Memorandum ANL/MCS– TM–163, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., 1992. ADIFOR Working Note # 7.

[Bisc91b] C. Bischof, A. Griewank, and D. Juedes, Exploiting parallelism in automatic differentiation, in Proceedings of the 1991 International Conference on Supercomputing, E. Houstis and Y. Muraoka, eds., ACM Press, Baltimore, Md., 1991, pp. 146–153. Also appeared as Preprint MCS–P204–0191, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., January 1991.

[Bisc91g] C. Bischof and P. Hovland, Using ADIFOR to compute dense and sparse Jacobians, Technical Memorandum ANL/MCS–TM–158, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., October 1991. ADIFOR Working Note # 2.

[Bisc91c] C. Bischof and J. Hu, Utilities for building and optimizing a computational graph for algorithmic decomposition, Technical Memorandum ANL/MCS–TM–148, Mathematics and Computer Sciences Division, Argonne National Laboratory, Argonne, Ill., April 1991.

[Bohl87a] G. Bohlender, C. Ullrich, J. Wolff von Gudenberg, and L. B. Rall, Pascal-SC, A Computer Language for Scientific Computation, Academic Press, New York, 1987.

[Bord56a] J. L. Bordewijk, Inter-reciprocity applied to electrical networks, Applied Science Research, The Netherlands, Sect. B, 6 (1956), pp. 1–74.

[Boyl90a] A. Boyle and B. F. Caviness, Future Directions for Research in Symbolic Computing, SIAM, Philadelphia, Penn., 1990.

[Brac68a] J. Bracken and G. P. McCormick, Selected Applications of Nonlinear Programming, John Wiley and Sons, New York, 1968.

[Bram61a] J. N. Bramhall, An iterative method for inversion of power series, Comm. ACM, 4 (1961), pp. 317–318, 503.

[Bren73a] R. P. Brent, Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, N.J., 1973.

[Bren77a] R. P. Brent and H. T. Kung, Fast algorithms for composition and reversion of multivariate power series, in Proceedings of the Conference on Theoretical Computer Science, University of Waterloo, Waterloo, Ontario, Canada, August 1977, 1977, pp. 149–158.

[Bren78a] , Fast algorithms for manipulating formal power series, J. ACM, 25 (1978), pp. 581–595.

[Bren80a] R. P. Brent and J. F. Traub, On the complexity of composition and generalized composition of power series, SIAM J. Comput., 9 (1980), pp. 54–66.

[Breu69a] M. A. Breuer, Generation of optimal code for expressions via factorization, Comm. ACM, 12 (1969), pp. 330–340.

[Broo88a] A. Brook, D. Kendrick, and A. Meerhaus, GAMS: A User’s Guide, Scientific Press, Redwood City, Calif., 1988.

[Broo83a] B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan, and M. Karplus, CHARMM: A program for macromolecular energy, minimization, and dynamics calculations, J. Computational Chemistry, 4 (1983), pp. 187– 217.

[Brow79a] K. L. Brown, The ion optical program TRANSPORT, Technical Report No. 91, SLAC, 1979.

[Brow64a] K. L. Brown, R. Belbeoch, and P. Bounin, First- and second-order magnetic optics matrix equations for the midplane of uniform-field wedge magnets, Review of Scientific Instruments, 35 (1964), pp. 481 +.

[Byrn87a] G. D. Byrne and A. C. Hindmarsh, Stiff ODE solvers: A review of current and coming attractions, J. Computational Physics, 70 (1987), pp. 1–62.

[Cacu81a] D. G. Cacuci, Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach, J. Math. Phys., 22 (1981), pp. 2794–2802.

[Cacu81b] , Sensitivity theory for nonlinear systems. II. Extension to additional classes of responses, J. Math. Phys., 22 (1981), pp. 2803–2812.

[Cacu84a] D. G. Cacuci and M. C. G. Hall, Efficient estimation of feedback effects with application to climate models, J. Atmos. Sci., 41 (1984), pp. 2063–2068.

[Call88a] D. Callahan, K. Cooper, R. T. Hood, K. Kennedy, and L. M. Torczon, ParaScope: A parallel programming environment, International J. Supercomputer Applications, 2 (1988).

[Camp92a] S. L. Campbell, E. Moore, and Y. Zhong, Utilization of automatic differentiation in control algorithms. Preprint for presentation at the 31st IEEE Conference on Decision and Control to be held December 16–18, 1992, in Tucson., 1992.

[Care87a] D. C. Carey, The Optics of Charged Particle Beams, Harwood, 1987.

[Carl86a] B. R. Carlile, Solution of nonlinear systems of equations on the FPS 64-bit family of scientific computers using automatic differentiation, in Proceedings of the 1986 Array Conference (Portland, Oregon), 1986, pp. 142–169.

[Cart74a] R. D. Carter, L. F. Kemp, Jr., A. C. Pierce, and D. L. Williams, Performance matching with constraints, Society of Petroleum Engineers J., (1974), pp. 187–196.

[Chan67a] Y. F. Chang, The conduction-diffusion theory of semiconductor junctions, J. Applied Physics, 38 (1967), pp. 534–544.

[Chan74a] , Automatic solution of differential equations, in Constructive and Computational Methods for Differential and Integral Equations, D. L. Colton and R. P. Gilbert, eds., vol. 430 of Lecture Notes in Mathematics, Springer Verlag, New York, 1974, pp. 61–94.

[Chan86a] , The ATOMCC toolbox, BYTE, 11 (1986), pp. 215–224.

[Chan91a] , A variable-order (10 – ∞) Taylor series method for solving ODE’s with integration steps almost equal to the radii of convergence. Poster presented at SIAM Workshop on Automatic Differentiation of Algorithms, Breckenridge, Colo., January 1991.

[Chan81a] Y. F. Chang, M. Tabor, J. Weiss, and G. F. Corliss, On the analytic structure of the Henon-Heiles system, Physics Letters, 85A (1981), pp. 211–213.

[Chao90a] W. C. Chao and L. P. Chang, Status of the development of a variational data assimilation system using the adjoint method at Goddard Laboratory for Atmospheres, in Proceedings of the International Symposium on Assimilation of Observations in Meteorology and Oceanography, World Meteorological Organization, Geneva, Switzerland, 1990, pp. 355–358.

[Char91a] B. W. Char, Computer algebra as a toolbox for program generation and manipulation, in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, A. Griewank and G. F. Corliss, eds., SIAM, Philadelphia, Penn., 1991, pp. 53–60.

[Char86a] B. W. Char, G. J. Fee, K. O. Geddes, G. H. Gonnet, and M. B. Monagan, A tutorial introduction to MAPLE, J. Symbolic Computation, 2 (1986), pp. 179– 200.

[Char91b] B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, Maple V Language Reference Manual, Springer Verlag, New York, 1991.

[Char91c] , Maple V Library Reference Manual, Springer Verlag, New York, 1991.

[Char88a] B. W. Char, K. O. Geddes, G. H. Gonnet, M. B. Monagan, and S. M. Watt, MAPLE Reference Manual, Watcom Publications, Waterloo, Ontario, Canada, 1988.

[Chav75a] G. Chavent, M. Dupuy, and P. Lemmonier, History matching by use of optimal theory, Society of Petroleum Engineers J., (1975), pp. 74–86.

[Chen74a] W. H. Chen, G. R. Gavalas, J. H. Seinfeld, and M. L. Wasserman, A new algorithm for automatic history matching, Society of Petroleum Engineers J., (1974), pp. 593–608.

[Chri91a] D. B. Christianson, Automatic Hessians by reverse accumulation in Ada, IMA J. on Numerical Analysis, (1991). Presented at SIAM Workshop on Automatic Differentiation of Algorithms, Breckenridge, Colo., January 1991.

[Chri91b] , Reverse accumulation and accurate rounding error estimates for Taylor series coefficients, Optimization Methods and Software, 1 (1991), pp. 81–94. Also appeared as Technical Report No. NOC TR239, The Numerical Optimisation Centre, University of Hertfordshire, U.K., July 1991.

[Chri92a] , Automatic Hessians by reverse accumulation, IMA J of Numerical Analysis, 12 (1992), pp. 135–150. Also appeared as Technical Report No. NOC TR228, The Numerical Optimisation Centre, University of Hertfordshire, U.K., April 1990.

[Chri92b] , Reverse accumulation and attractive fixed points, Technical Report NOC TR 258, The Numerical Optimisation Centre, University of Hertfordshire, Hatfield, UK, March 1992.

[Civa65a] P. P. Civalleri, Cohn’s generalized theorem, Alta Frequenza, 35 (1965), pp. 797–806.

[Clar83a] F. H. Clark, Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, 1983.

[Cole84a] T. F. Coleman, B. S. Garbow, and J. J. Moré, Software for estimating sparse Jacobian matrices, ACM Trans. Math. Software, 10 (1984), pp. 329–345.

[Cole83a] T. F. Coleman and J. J. Moré, Estimation of sparse Jacobian matrices and graph coloring problems, SIAM J. on Numerical Analysis, 20 (1984), pp. 187–209.

[Cont80a] S. D. Conte and C. de Boor, Elementary Numerical Analysis, McGraw-Hill, New York, 1980.

[PROS77a] Control Data Corporation, PROSE – A General Purpose Higher Level Language, 1977. Procedure Manual (Pub. No. 84003000 Rev. B), Calculus Operations Manual (Pub. No. 84003200 Rev. A), Calculus Applications Guide (Pub. No. 84000170 Rev. A).

[Cook88a] G. O. Cook, Jr., ALPAL, a tool for the development of large-scale simulation codes, Technical Report UCID-21482, Lawrence Livermore National Laboratory, Berkeley, Calif., August 1988.

[Corl91c] R. M. Corless and G. F. Corliss, Automatic differentiation in validated defect control for ordinary differential equations. Poster presented at SIAM Workshop on Automatic Differentiation of Algorithms, Breckenridge, Colo., January 1991.

[Corl92a] G. Corliss, A. Griewank, T. Robey, and S. Wright, Automatic differentiation applied to unsaturated flow — ADOL–C case study, Technical Memorandum ANL/MCS–TM–162, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., April 1992.

[Corl87b] G. F. Corliss, Performance of self-validating quadrature, in Proceedings of the NATO Advanced Workshop on Numerical Integration: Recent Developments, Software, and Applications, P. Keast and G. Fairweather, eds., Reidel, Boston, 1987, pp. 239–259.

[Corl88a] , Applications of differentiation arithmetic, in Reliability in Computing, R. E. Moore, ed., Academic Press, London, 1988, pp. 127–148.

[Corl91d] , Automatic differentiation bibliography, in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, A. Griewank and G. F. Corliss, eds., SIAM, Philadelphia, Penn., 1991, pp. 331–353.

[Corl91a] , Overloading point and interval Taylor operators, in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, A. Griewank and G. F. Corliss, eds., SIAM, Philadelphia, Penn., 1991, pp. 139–146.

[Corl82a] G. F. Corliss and Y. F. Chang, Solving ordinary differential equations using Taylor series, ACM Trans. Math. Software, 8 (1982), pp. 114–144.

[Corl88b] G. F. Corliss, P. H. Davis, and G. S. Krenz, Bibliography on interval methods for the solution of ordinary differential equations, Technical Report No. 289, Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisc., September 1988.

[Corl84a] G. F. Corliss and L. B. Rall, Automatic generation of Taylor series in Pascal-SC: Basic operations and applications to differential equations, in Trans. of the First Army Conference on Applied Mathematics and Computing (Washington, D.C., 1983), ARO Rep. 84-1, U. S. Army Res. Office, Research Triangle Park, N.C., 1984, pp. 177– 209.

[Corl87a] , Adaptive, self-validating quadrature, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 831–847.

[Corl91b] , Computing the range of derivatives, in Computer Arithmetic, Scientific Computation, and Mathematical Modelling, E. Kaucher, S. M. Markov, and G. Mayer, eds., vol. 12 of IMACS Annals on Computing and Applied Mathematics, J. C. Baltzer AG, Basel, 1991, pp. 195–212.

[Cour85a] P. Courtier, Experiments in data assimilation using the adjoint model technique, in Proceedings of the Workshop on High-Resolution Analysis ECMWF (UK), June 1985.

[Cour87b] , Application of optimal control to numerical meteorological forecasting, Doctoral thesis, Université Pierre-et-Marie-Curie, Paris, France, 1987. (In French).

[Cour87a] P. Courtier and O. Talagrand, Variational assimilation of meteorological observations with the adjoint equation – Part II. Numerical results, Q. J. R. Meteorol. Soc., 113 (1987), pp. 1329–1347.

[Cour90a] , Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations, Tellus, 42A (1990), pp. 531–549.

[Cour90b] P. Courtier, J. N. Thepaut, and O. Talagrand, 4-dimensional data assimilation using the adjoint of a primitive equation model, in Proceedings of the International Symposium on Assimilation of Observations in Meteorology and Oceanography, World Meteorological Organization, Geneva, Switzerland, 1990, pp. 337–340.

[Crar75a] F. D. Crary, The AUGMENT precompiler. II. Technical documentation, MRC Technical Summary Report No. 1470, Mathematics Research Center, University of Wisconsin-Madison, 1975.

[Crar76a] , The AUGMENT precompiler. I. User information, MRC Technical Summary Report No. 1469, Mathematics Research Center, University of Wisconsin-Madison, 1976.

[Crar79a] , A versatile precompiler for nonstandard arithmetics, ACM Trans. Math. Software, 5 (1979), pp. 204–217.

[Datt91a] S. Datta, J. Nugent, A. Tishler, and J. L. Wang, Seasonality, differential access, and interlinking of labour and credit, J. Development Studies, (to appear).

[Davi81a] A. J. T. Davie and R. Morrison, Recursive Descent Compiling, Ellis-Horwood, Chichester, 1981.

[Davi88a] P. H. Davis, G. F. Corliss, and G. S. Krenz, A bibliography on methods and techniques in differentiation arithmetic, Technical Report AM–88–09, School of Mathematics, University of Bristol, Bristol, U.K., 1988.

[Davi87a] P. H. Davis and J. D. Pryce, A new implementation of automatic differentiation for use with numerical software, Technical Report AM–87–11, School of Mathematics, University of Bristol, Bristol, U.K., 1987.

[Davi92a] P. H. Davis, J. D. Pryce, and B. Stephens, Recent developments in automatic differentiation, in Scientific Software Systems, J. C. Mason and M. G. Cox, eds., Chapman and Hall, 11 New Fetter Lane, London EC4P 4EE, 1990, pp. 153–165.

Also appeared as Technical Report ACM–89–1, Royal Military College of Science at Shrivenham, Shrivenham, U.K.

[Davi88b] P. H. Davis, B. Stephens, G. F. Corliss, and G. S. Krenz, Specification of a preprocessor for use with differentiation arithmetic, Technical Report AM–88–08, School of Mathematics, University of Bristol, Bristol, U.K., September 1988.

[Denn81a] J. Dennis, D. Gay, and R. E. Welsch, Algorithm 573. NL2SOL — An adaptive nonlinear least-squares algorithm, ACM Trans. Math. Software, 7 (1981), pp. 369–383.

[Denn83a] J. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, N.J., 1983.

[Derb85a] J. C. Derber, The Variational 4-D Assimilation of Analyses Using Filtered Models as Constraints, PhD thesis, University of Wisconsin-Madison, Madison, Wisc., 1985.

[Dewa89a] M. C. Dewar, IRENA — An integrated symbolic and numerical computational environment, in Proceedings of the 1989 International Symposium on Symbolic and Algebraic Computation, G. H. Gonnet, ed., 1989, pp. 171–179.

[Dewa90a] M. C. Dewar and M. G. Richardson, Reconciling symbolic and numeric computation in a practical setting, in Design and Implementation of Symbolic Computing Systems, Proceedings of DISCO 90, A. Miola, ed., vol. 429 of Lecture Notes in Computer Science, Springer Verlag, Berlin, April 1990, pp. 195–204.

[Dixo87a] L. C. W. Dixon, Automatic differentiation and parallel processing in optimisation, Technical Report No. 180, The Numerical Optimisation Center, Hatfield Polytechnic, Hatfield, U.K., 1987.

[Dixo91a] , Use of automatic differentiation for calculating Hessians and Newton steps, in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, A. Griewank and G. F. Corliss, eds., SIAM, Philadelphia, Penn., 1991, pp. 114– 125.

[Dixo86c] L. C. W. Dixon, P. Dolan, and R. C. Price, Finite element optimisation: The use of structured automatic differentiation, Technical Report No. 175, The Numerical Optimisation Center, Hatfield Polytechnic, Hatfield, U.K., 1986.

[Dixo87c] L. C. W. Dixon and Z. Maany, The echelon method for the solution of sparse sets of linear equations, Technical Report NOC TR177, The Numerical Optimisation Center, Hatfield Polytechnic, Hatfield, U.K., February 1988.

[Dixo89b] , The performance of the truncated Newton, conjugate gradient algorithm in Fortran and Ada, Technical Report NOC TR210, The Numerical Optimisation Center, Hatfield Polytechnic, Hatfield, U.K., June 1989.

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