Automatic Differentiation of Computer Programs

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Automatic Differentiation of Computer Programs

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 6 , Issue 2 (June 1980) table of contents

Pages: 150 - 165

Year of Publication: 1980

ISSN:0098-3500

Author

Gershon Kedem

Department of Computer Science and Laboratory for Laser Energetics, Mathematical Sciences Building, University of Rochester, Rochester, NY

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 3, Downloads (12 Months): 42, Citation Count: 17

Additional Information:

references cited by index terms collaborative colleagues

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BARTON, D, WILLER, I.M, AND ZAHAR, R.V.M. Taylor series method for ordinary differential equations' An evaluation. Mathematical Software, Academic Press, New York, 1971.
	2	BRAUN, J.A, AND MOORE, R E. A program for the solution of differential equations using interval arithmetic (DIFEQ) for the CDC3600 and 1604. MRC Tech. Summary Rep. 901, Math. Res. Cent., Univ. Wisconsin-Madison, June 1968.
	3	Fred D. Crary, A Versatile Precompiler for Nonstandard Arithmetics, ACM Transactions on Mathematical Software (TOMS), v.5 n.2, p.204-217, June 1979 [doi>10.1145/355826.355834]
	4	CRARY, F.D. The AUGMENT precompfler' I. User information. MRC Tech. Summary Rep. 1469, Math Res. Cent., Univ. Wisconsin-Madison, Dec 1974.
	5	CRARY, V D. The AUGMENT Precompiler: ii. Technical documentation MRC Tech. Summary Rep. 1420, Math Res. Cent., Univ. Wisconsin-Madison, Oct. 1975.
	6	GRAY, J., AND RALL, L.B. NEWTON" A general purpose program for solving nonlinear systems. MRC Tech Summary Rep 790, Math. Res. Cent., Univ. Wisconsin-Madison, Sept. 1967
	7	KNAPP, H., AND WANNER, G. LIESE II. A program for ordinary chfferential equations using Lie- Series MRC Tech Summary Rep. 1008, Math. Res. Cent., Univ. Wisconsin-Madison, March 1970
	8	KRASNOSEL'SKII, M A, ET AL. Approximate Solutton of Operator Equations. Wolters-Noordhoff, Groningen, 1972.
	9	KUBA, D., AND RALL, L.B. A UNIVAC 1108 program for obtaining rigorous error estimates for approximate soluUon of systems of equations. MRC Tech. Summary Rep 1168, Math. Res. Cent, Umv. Wisconsin-Madison, Jan. 1972.
	10	MOORE, R E Interval Analysts. PrenUce-Hall, Englewood Chffs, N.J., 1966.
	11	MOORE, R.E.The Automattc Analysts and Control of Error ~n D~gttal Computatton, vol. 1, L. B. Rail (Ed.) Wiley, New York, 1965.
	12	PUGH, R.E A language for nonlinear programming problems. Math. Program. 2, 2 (1972), 176- 206.
	13	REITER, A. Automatic generation of Taylor coefficients (TAYLOR) for the CDC1604. MRC Tech. Summary Rep. 830, Math. Res Cent., Univ. Wisconsin-Madison, Nov 1967
	14	REITER, A, AND GRAY, J. Compiler of chfferentiable expressions (CODEX) for the CDC3600. MRC Tech Summary Rep. 791, Math. Res. Cent., Umv. Wisconsin-Madison, Dec. 1967.
	15	Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill, Inc., New York, NY, 1987
	16	WARNER, D.D A partial derivative generator. Comput. Sci. Tech. Rep 28, Bell Lab., Murray Hill, N.J., April 1975.
	17	WERTZ, H J. SUPER-CODEX: Analytm differentiation of FORTRAN statements. Aerospace Rep. TOR-0172(9320)-12, Aerospace Corp., Los Angeles, Calif., June 1972.

CITED BY 17

	Richard D. Neidinger, An efficient method for the numerical evaluation of partial derivatives of arbitrary order, ACM Transactions on Mathematical Software (TOMS), v.18 n.2, p.159-173, June 1992
	George Corliss , Gary Krenz, Indefinite integration with validation, ACM Transactions on Mathematical Software (TOMS), v.15 n.4, p.375-393, Dec. 1989
	George Corliss , Y. F. Chang, Solving Ordinary Differential Equations Using Taylor Series, ACM Transactions on Mathematical Software (TOMS), v.8 n.2, p.114-144, June 1982
	Andreas Griewank , David Juedes , Jean Utke, Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++, ACM Transactions on Mathematical Software (TOMS), v.22 n.2, p.131-167, June 1996
	Richard D. Neidinger, Differential equations are recurrence relations in APL, ACM SIGAPL APL Quote Quad, v.23 n.1, p.165-174, July 1992
	Fred D. Crary, A Versatile Precompiler for Nonstandard Arithmetics, ACM Transactions on Mathematical Software (TOMS), v.5 n.2, p.204-217, June 1979
	J. A. van Hulzen, Breuer's grow factor algorithm in computer algebra, Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, p.100-104, August 05-07, 1981, Snowbird, Utah, United States
	L B. Rall, Differentiation in PASCAL-SC: type GRADIENT, ACM Transactions on Mathematical Software (TOMS), v.10 n.2, p.161-184, June 1984
	Annie A. M. Cuyt , L. B. Rall, Computational implementation of the multivariate Halley method for solving nonlinear systems of equations, ACM Transactions on Mathematical Software (TOMS), v.11 n.1, p.20-36, March 1985
	Michael B. Monagan , Walter M. Neuenschwander, GRADIENT: algorithmic differentiation in Maple, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, p.68-76, July 06-08, 1993, Kiev, Ukraine
	M. Dobmann , M. Liepelt , K. Schittkowski, Algorithm 746: PCOMP--a Fortran code for automatic differentiation, ACM Transactions on Mathematical Software (TOMS), v.21 n.3, p.233-266, Sept. 1995
	F. D. Crary , J. M. Yohe, The AUGMENT precompiler as a tool for the development of special purpose arithmetic packages, ACM SIGNUM Newsletter, v.14 n.1, p.53-56, March 1979
	J. H. J. Molenkamp , V. V. Goldman , J. A. van Hulzen, An improved approach to automatic error cumulation control, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.414-418, July 15-17, 1991, Bonn, West Germany
	João Batista Oliveira, Evaluating Lipschitz Constants for Functions Given by Algorithms, Computational Optimization and Applications, v.16 n.3, p.215-229, Sept. 2000
	F W Pfeiffer, Automatic differentiation in prose, ACM SIGNUM Newsletter, v.22 n.1, p.2-8, Jan. 1987
	Barak A. Pearlmutter , Jeffrey Mark Siskind, Reverse-mode AD in a functional framework: Lambda the ultimate backpropagator, ACM Transactions on Programming Languages and Systems (TOPLAS), v.30 n.2, p.1-36, March 2008
	Uwe Naumann , Yuxiao Hu, Optimal vertex elimination in single-expression-use graphs, ACM Transactions on Mathematical Software (TOMS), v.35 n.1, p.1-20, July 2008

INDEX TERMS

Primary Classification:
G. Mathematics of Computing

Additional Classification:
D. Software
D.3 PROGRAMMING LANGUAGES
D.3.2 Language Classifications

Nouns: FORTRAN
D.3.3 Language Constructs and Features
Subjects: Procedures, functions, and subroutines

G. Mathematics of Computing

General Terms:
Languages, Theory

Collaborative Colleagues:

Gershon Kedem: colleagues

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