Integer Arithmetic Algorithms for Polynomial Real Zero Determination

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Integer Arithmetic Algorithms for Polynomial Real Zero Determination

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Journal of the ACM (JACM) archive
Volume 18 , Issue 4 (October 1971) table of contents

Pages: 533 - 548

Year of Publication: 1971

ISSN:0004-5411

Author

Lee E. Heindel

Bell Telephone Laboratories, Inc., Holmdel, New Jersey and University of Wisconsin, Computer Sciences Department, Madison, Wisconsin

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 3, Downloads (12 Months): 34, Citation Count: 16

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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	COLLINS, G.E. Computing time analyses for some arithmetic and algebraic algorithms. Proc. 1968 Summer Institute on Symbolic Mathematical Computation. R. G. Tobey, Ed., IBM Boston Programming Center (June 1969), pp. 195-231.
	2	COLLINS, G.E. Algebraic Algorithms. Prentice-Hall, Englewood Cliffs, N.J. (to be published).
	3	George E. Collins, The calculation of multivariate polynomial resultants, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, p.212-222, March 23-25, 1971, Los Angeles, California, United States [doi>10.1145/800204.806289]
	4	Lee Edward Heindel, Algorithms for exact polynomial root calculation, 1971
	5	HURWITZ, A. Uber den Satz von Budan-Fourier, Math. Ann. 71 (1912), 584-591.
	6	Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
	7	TARSKI, A. A Decision Method for Elementary Algebra and Geometry. U. of California Press, Berkeley, 1951.
	8	WILF, H.S. Mathematics for the Physical Sciences. Wiley, New York, 1962.

CITED BY 16

	Attilio Colagrossi , Alfonso M. Miola, Computing real zeros of polynomials with parametric coefficients, ACM SIGSAM Bulletin, v.17 n.1, p.12-15, February 1983
	Siegfried Rump, On the sign of a real algebraic number, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.238-241, August 10-12, 1976, Yorktown Heights, New York, United States
	J H Davenport, A :20piano movers' ', ACM SIGSAM Bulletin, v.20 n.1-2, p.15-17, Feb/May 1986
	George E. Collins , Alkiviadis G. Akritas, Polynomial real root isolation using Descarte's rule of signs, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.272-275, August 10-12, 1976, Yorktown Heights, New York, United States
	Richard J. Fateman, An Algorithm for Deciding the Convergence of the Rational Iteration xn+1= f(xn), ACM Transactions on Mathematical Software (TOMS), v.3 n.3, p.272-278, Sept. 1977
	George E. Collins , Rüdiger Loos, Polynomial real root isolation by differentiation, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.15-25, August 10-12, 1976, Yorktown Heights, New York, United States
	Alkiviadis G. Akritas, A new method for polynomial real root isolation, Proceedings of the 16th annual Southeast regional conference, p.39-43, April 13-15, 1978, Atlanta, Georgia
	Alkiviadis G. Akritas, A short note on a new method for polynomial real root isolation, ACM SIGSAM Bulletin, v.12 n.4, p.12-13, November 1978
	David Y. Y. Yun, On algorithms for solving systems of polynomial equations, ACM SIGSAM Bulletin
	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
	George E. Collins, Quantifier elimination for real closed fields by cylindrical algebraic decomposition--preliminary report, ACM SIGSAM Bulletin, v.8 n.3, p.80-90, August 1974
	M Ben-Or , E Feig , D Kozen , P Tiwari, A fast parallel algorithm for determining all roots of a polynomial with real roots, Proceedings of the eighteenth annual ACM symposium on Theory of computing, p.340-349, May 28-30, 1986, Berkeley, California, United States
	John Keyser , Shankar Krishnan , Dinesh Manocha, Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic, Proceedings of the fourth ACM symposium on Solid modeling and applications, p.42-55, May 14-16, 1997, Atlanta, Georgia, United States
	James R. Pinkert, An Exact Method for Finding the Roots of a Complex Polynomial, ACM Transactions on Mathematical Software (TOMS), v.2 n.4, p.351-363, Dec. 1976
	B. F. Caviness , G. E. Collins, Symbolic mathematical computation in a Ph.D. computer science program, Proceedings of the second SIGCSE technical symposium on Education in computer science, p.19-23, March 01-01, 1972
	B. F. Caviness , G. E. Collins, Symbolic mathematical computation in a Ph. D. computer science program, ACM SIGCSE Bulletin, v.4 n.1, March 1972