Abstract
We present a parallel implementation of the coefficient sign variation method for polynomial real root isolation. The implementation uses PARSAC-2, a parallel version, based on threads, of the SAC-2 computer algebra system. A discussion of the implementation and its performance is given. Our timing results were obtained on a shared memory multiprocessor implementation using the Encore Multimax.
Preview
Unable to display preview. Download preview PDF.
References
A. Akritas and G. E. Collins. Polynomial real root isolation using Descartes' rule of signs. In Proceedings of SYMSAC 76, pages 272–275. ACM, New York, 1976.
A. T. Bharucha-Reid. Random algebraic equations. In A. T. Bharucha-Reid, editor, Probabilistic Methods in Applied Mathematics, volume 2, pages 1–52. Academic Press, 1970.
G.E.Collins. Computer algebra of polynomials and rational functions. American Mathematical Monthly, 80(7):725–755, August–September 1973.
G. E. Collins and E. Horowitz. The minimum root separation of a polynomial. Math. Comp., 28(126):589–597, April 1974.
G. E. Collins and J. R. Johnson. Quantifier elimination and the sign variation method for real root isolation. In Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, pages 264–271. ACM, 1989.
G. E. Collins and R. Loos. Real zeros of polynomials. In B. Buchberger, G. E. Collins, and R. Loos, editors, Computer Algebra, pages 83–94. Springer-Verlag, Wien-New York, 1982.
G. E. Collins and R. G. K. Loos. SAC-2 system documentation. Technical report. In Europe available from: R. G. K. Loos, Universität Tübingen, Informatik, D-7400 Tübingen, W-Germany. In the U.S. available from: G. E. Collins, Ohio State University, Computer Science, Columbus, OH 43210, U.S.A.
E. C. Cooper and R. P. Draves. C threads. Technical report, Computer Science Department, Carnegie Mellon University, Pittsburg, PA 15213, July 1987.
J. H. Davenport. Computer algebra for cylindrical algebraic decomposition. Technical report, The Royal Institute of Technology, Dept. of Numerical Analysis and Computing Science, S-100 44, Stockholm, Sweden, 1985.
Encore Computer Corp. Multimax Technical Summary, 726-01759 Rev. E edition, January 1989.
J. R. Johnson. Algorithms for Polynomial Real Root Isolation. PhD thesis, The Ohio State University, 1991. Dissertation in preparation.
M. Kac. On the average number of real roots of a random algebraic equation. Bulletin of the American Mathematical Society, 49:314–320, 938, 1943.
D. E. Knuth. The Art of Computer Programming (Seminumerical Algorithms), volume 2. Addison-Wesley, Reading, Mass., 1st edition, 1969.
Wolfgang W. Küchlin. PARSAC-2: A parallel SAC-2 based on threads. In Proc. AAECC-8, LNCS, Tokyo, Japan, August 1990. Springer-Verlag. To appear.
Wolfgang W. Küchlin. The S-threads environment for parallel symbolic computation. Chapter 1, these proceedings.
K. Mahler. An inequality for the discriminant of a polynomial. Michigan Mathematics Journal, 11(3):257–262, September 1964.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Collins, G.E., Johnson, J.R., Küchlin, W. (1992). Parallel real root isolation using the coefficient sign variation method. In: Zippel, R.E. (eds) Computer Algebra and Parallelism. CAP 1990. Lecture Notes in Computer Science, vol 584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55328-2_6
Download citation
DOI: https://doi.org/10.1007/3-540-55328-2_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55328-1
Online ISBN: 978-3-540-47026-7
eBook Packages: Springer Book Archive