Differentiation in PASCAL-SC: type GRADIENT

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Differentiation in PASCAL-SC: type GRADIENT

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 10 , Issue 2 (June 1984) table of contents

Pages: 161 - 184

Year of Publication: 1984

ISSN:0098-3500

Author

L B. Rall

University of Wisconsin at Madison

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 2, Downloads (12 Months): 19, Citation Count: 7

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references cited by index terms review 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	BOHLENDER, G., GRUNER, K., KAUCHER, E., KLATTE, R., KRAMER, W., KULISCH, U. w., RUMP, S. M., ULLRICH, C., WOLFF VON GUDENBERG, J. AND MIRANDER., W.L. Pascal-SC: A Pascal for scientific computahon. Res. Rep. RC 9009, IBM Thomas J. Watson Research Center, Yorktown Heights, N. Y., 1981.
	2	William James Cody, Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics), Prentice-Hall, Inc., Upper Saddle River, NJ, 1980
	3	J. E. Dennis, Jr. , Robert B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16), Soc for Industrial & Applied Math, 1996
	4	GRAY, J. H. AND RALL, L.B. NEWTON: A general purpose program for solving nonhnear systems. In Proceedings of the 1967 Army Numerwal Analysis Conference, U. S. Army Research Office, Durham, N. C., 1967, pp. 11-59.
	5	GRAY, J. H. AND REITER, A. Compiler of differential expressions (CODEX) for the CDC 3600. Techmcal Summary Report 791, Mathematics Research Center, University of Wisconsin at Madison, Madison, Wlsc., 1967.
	6	Kathleen Jensen , Niklaus Wirth, Pascal-User Manual and Report, Springer-Verlag New York, Inc., Secaucus, NJ, 1975
	7	Gershon Kedem, Automatic Differentiation of Computer Programs, ACM Transactions on Mathematical Software (TOMS), v.6 n.2, p.150-165, June 1980 [doi>10.1145/355887.355890]
	8	KUBA, D. AND RALL, L.B. A UNIVAC 1108 program for obtaining rigorous error bounds for approximate solutions of systems of equations. Technical Summary Report 1168, Mathematics Research Center, University of Wisconsin at Madison, Madison, Wisc., 1972.
	9	Ulrich W. Kulisch , Willard L. Miranker, Computer Arithmetic in Theory and Practice, Academic Press, Inc., Orlando, FL, 1981
	10	MILNE, W.E. Numerwal Calculus. Princeton University Press, Princeton, N. J., 1949.
	11	RALL, L.B. Computational Solution of Nonlinear Operator Equations. Wiley, New York, 1969. Reprinted by Krieger, Huntington, N. Y., 1979.
	12	RALL, L.B. Applications of software for automatic differentiation m numerical computation. Computmg, Suppl. 2 (1980), 141-156.
	13	RALL, L B. Automatic Differentiation" Techmques andApphcations. Lecture Notes in Computer Science, vol. 120, Springer-Verlag, New York, 1981.
	14	ROSSER, J. B. AND DE BOOR, C. Pocket Calculator Supplement for Calculus. Addison-Wesley, Reading, Mass., 1979.
	15	RUTISHAUSER, H. Description of ALGOL-60 Springer-Verlag, New York, 1967.
	16	SOKOLNIKOFF, E. S. AND SOKOLNIKOFF, I.S. Higher Mathematics for Engineers and Physicists. McGraw-Hall, New York, 1945.
	17	TIKtlONOV, A. N. AND ARSENIN, V.Y. Solutions of Ill-Posed Problems. (English Translation edited by Fritz John), Winston, Washington, D. C., 1977.
	18	WOLFF VON GUDENBERG, J. Einbettung allgemeiner Rechnerarithmetik in Pascal mittels eines Operatorkonzeptes und Implementierung der Standardfunktionen mit optimaler Genauigkelt. (Imbedding of a general computer arithmetic in Pascal by means of an operator concept and the implementation of the standard functions with optimal accuracy.) Ph.D. dissertation, University of Karlsruhe, West Germany, 1980.
	19	WOLFF VON GUDENBERG, J. Gesamte Ar~thmet~k des PascaI-SC Rechners. Benutzerhandbuch (Complete Arithmetic of the Pascal-SC Computer: User Handbook) Institute for Applied Mathematics, University of Karlsruhe, West Germany, 1981.

CITED BY 7

	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
	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
	R. D. Neidinger, An APL approach to differential calculus yields a powerful tool, ACM SIGAPL APL Quote Quad, v.19 n.4, p.285-288, Aug. 1989
	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
	Thomas W. Reps , Louis B. Rall, Computational Divided Differencing and Divided-Difference Arithmetics, Higher-Order and Symbolic Computation, v.16 n.1-2, p.93-149, March-June 2003
	F W Pfeiffer, Automatic differentiation in prose, ACM SIGNUM Newsletter, v.22 n.1, p.2-8, Jan. 1987
	Max E. Jerrell, Automatic differentiation using almost any language, ACM SIGNUM Newsletter, v.24 n.1, p.2-10, January 1989

INDEX TERMS

Classification:
D. Software
D.3 PROGRAMMING LANGUAGES
D.3.3 Language Constructs and Features
Subjects: Data types and structures

G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.5 Roots of Nonlinear Equations
Subjects: Systems of equations
G.1.6 Optimization
Subjects: Gradient methods

I. Computing Methodologies
I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
I.1.3 Languages and Systems

Nouns: PASCAL-SC

General Terms:
Algorithms, Languages

REVIEW

"Richard V. Andree : Reviewer"

The well-documented inaccuracies that arise when numerical differentiation is used in scientific and engineering computations of even moderate size suggest that actual derivatives should be used instead. Human error frequently rears its head in more...

Collaborative Colleagues:

L B. Rall: colleagues

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