Chains of recurrences—a method to expedite the evaluation of closed-form functions

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Chains of recurrences—a method to expedite the evaluation of closed-form functions

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the international symposium on Symbolic and algebraic computation table of contents

Oxford, United Kingdom

Pages: 242 - 249

Year of Publication: 1994

ISBN:0-89791-638-7

Authors

Olaf Bachmann	Dept. of Math. and Computer Science, Kent State University Kent, Ohio
Paul S. Wang	Distributed Computing Department, Sandia National Laboratories, P.O.Box 969 Mail Stop 9214, Livermore, CA
Eugene V. Zima	Dept. of Computational Mathematics and Cybernetics (BMK), Moscow State University, Moscow, 119899, Russia

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 26, Citation Count: 10

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ABSTRACT

Chains of Recurrences (CR's) are introduced as an effective method to evaluate functions at regular intervals. Algebraic properties of CR's are examined and an algorithm that constructs a CR for a given function is explained. Finally, an implementation of the method in MAXIMA/Common Lisp is discussed.

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	William H. Beyer. CRC Standard Mathematical Tables. CRC Press Inc., Boca Raton, Florida, 27th edition, 1984.
	2	The MATHLAB Group. Macsyma Reference Manual, version nine. Laboratory for Computer Science, M.I.T., Cambridge Mass., 1977.
	3	Donald E. Knuth. Seminumerical Algorithms, volume 2 of The Art of Computer Programming. Reading Mass.:Addison Wesley, 1981.
	4	Peter A. Stark. Introduction to N,t~'ne~4cal Methods. The Macmillan Company, New York, 1970.
	5	Paul S. Wang, A System Independent Graphing Package for Mathematical Functions, Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems, p.245-254, April 10-12, 1990
	6	Eugene V. Zima, Recurrent Relations and Speed-up of Computations Using Computer Algebra Systems, Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems, p.152-161, April 13-15, 1992

CITED BY 10

	Eugene V. Zima, Simplification and optimization transformations of chains of recurrences, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.42-50, July 10-12, 1995, Montreal, Quebec, Canada
	V. Kislenkov , V. Mitrofanov , E. Zima, Multidimensional chains of recurrences, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.199-206, August 13-15, 1998, Rostock, Germany
	Robert van Engelen , David Whalley , Xin Yuan, Validation of code-improving transformations for embeded systems, Proceedings of the 2003 ACM symposium on Applied computing, March 09-12, 2003, Melbourne, Florida
	Sergei A. Abramov , Manuel Bronstein , Marko Petkovšek, On polynomial solutions of linear operator equations, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.290-296, July 10-12, 1995, Montreal, Quebec, Canada
	Eugene V. Zima, On computational properties of chains of recurrences, Proceedings of the 2001 international symposium on Symbolic and algebraic computation, p.345, July 2001, London, Ontario, Canada
	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
	Robert A. van Engelen , J. Birch , Y. Shou , B. Walsh , Kyle A. Gallivan, A unified framework for nonlinear dependence testing and symbolic analysis, Proceedings of the 18th annual international conference on Supercomputing, June 26-July 01, 2004, Malo, France
	Robert van Engelen , David Whalley , Xin Yuan, Automatic validation of code-improving transformations on low-level program representations, Science of Computer Programming, v.52 n.1-3, p.257-280, August 2004
	Dinakar Dhurjati , Sumant Kowshik , Vikram Adve , Chris Lattner, Memory safety without garbage collection for embedded applications, ACM Transactions on Embedded Computing Systems (TECS), v.4 n.1, p.73-111, February 2005
	Yixin Shou , Robert A. van Engelen, Automatic SIMD vectorization of chains of recurrences, Proceedings of the 22nd annual international conference on Supercomputing, June 07-12, 2008, Island of Kos, Greece