Asymptotically fast computation of subresultants

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Asymptotically fast computation of subresultants

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1997 international symposium on Symbolic and algebraic computation table of contents

Kihei, Maui, Hawaii, United States

Pages: 233 - 240

Year of Publication: 1997

ISBN:0-89791-875-4

Author

Daniel Reischert

Institut für Informatik II, University of Bonn, Römerstraβe 164, D-53117 Bonn, Germany

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 3, Downloads (12 Months): 21, Citation Count: 6

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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	W. S. Brown, On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors, Journal of the ACM (JACM), v.18 n.4, p.478-504, Oct. 1971 [doi>10.1145/321662.321664]
	2	George E. Collins, Subresultants and Reduced Polynomial Remainder Sequences, Journal of the ACM (JACM), v.14 n.1, p.128-142, Jan. 1967 [doi>10.1145/321371.321381]
	3	George E. Collins, The Calculation of Multivariate Polynomial Resultants, Journal of the ACM (JACM), v.18 n.4, p.515-532, Oct. 1971 [doi>10.1145/321662.321666]
	4	George E. Collins , Rudiger Loos, Real zeroes of polynomials, Computer algebra: symbolic and algebraic computation (2nd ed.), Springer-Verlag New York, Inc., New York, NY, 1983
	5	HABICI~T, W. Eine Verallgemeinerung des Sturmschen Wurzelziihlverfahrens. Comm. Math. Helvetici 21 (1948), 99-116.
	6	KNUTH, D.E. The Analysis of Algorithms. Proc. In. ternat. Congress Math. (Nice, 1970), Vol. 3, Gauthier- Villars, Paris, 1971, pp. 269-274.
	7	Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
	8	LICKTEIG, T., AND Roy, M.-F. Cauchy Index Computation. To appear in Calcolo (1997).
	9	LOON, R. Generalized Polynomial Remainder Sequences. In Computer Algebra, Symbolic and Algebraic Computation, B. Buchberger, G.E. Collins, R. LooN, Eds. Springer-Verlag, Wien, 2nd ed, 1982, pp. 115-137.
	10	SCH6NnACE, A. Schnelle Berechnung yon Kettenbruchentwicklungen. Acta inform. 1 (1971), 139-144.
	11	A. Schönhage, Probabilistic computation of integer polynomial GCDs, Journal of Algorithms, v.9 n.3, p.365-371, September 1988 [doi>10.1016/0196-6774(88)90027-2]
	12	Arnold Schönhage , Ekkehart Vetter, A New Approach to Resultant Computations and Other Algorithms with Exact Division, Proceedings of the Second Annual European Symposium on Algorithms, p.448-459, September 26-28, 1994
	13	J. T. Schwartz, Fast Probabilistic Algorithms for Verification of Polynomial Identities, Journal of the ACM (JACM), v.27 n.4, p.701-717, Oct. 1980 [doi>10.1145/322217.322225]
	14	STRASSEN, V. The Computational Complexity of Continued Fractions. SIA M J. Comput. 12, 1 (1983), 1-27.

CITED BY 6

	M'hammed El Kahoui, An elementary approach to subresultants theory, Journal of Symbolic Computation, v.35 n.3, p.281-292, March 2003
	Joachim von zur Gathen , Thomas Lücking, Subresultants revisited, Theoretical Computer Science, v.297 n.1-3, p.199-239, 17 March 2003
	Arno Eigenwillig , Vikram Sharma , Chee K. Yap, Almost tight recursion tree bounds for the Descartes method, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy
	Philippe Saux Picart , Cyril Brunie, Symmetric subresultants and applications, Journal of Symbolic Computation, v.42 n.9, p.884-919, September, 2007
	Dimitrios I. Diochnos , Ioannis Z. Emiris , Elias P. Tsigaridas, On the complexity of real solving bivariate systems, Proceedings of the 2007 international symposium on Symbolic and algebraic computation, July 29-August 01, 2007, Waterloo, Ontario, Canada
	Dimitrios I. Diochnos , Ioannis Z. Emiris , Elias P. Tsigaridas, On the asymptotic and practical complexity of solving bivariate systems over the reals, Journal of Symbolic Computation, v.44 n.7, p.818-835, July, 2009