An Exact Method for Finding the Roots of a Complex Polynomial

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

An Exact Method for Finding the Roots of a Complex Polynomial

Full text

Pdf (752 KB)

Source

ACM Transactions on Mathematical Software (TOMS) archive
Volume 2 , Issue 4 (December 1976) table of contents

Pages: 351 - 363

Year of Publication: 1976

ISSN:0098-3500

Author

James R. Pinkert

Computer Science Department, University of Tennessee, Knoxville, TN

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 8, Downloads (12 Months): 73, Citation Count: 4

Additional Information:

references cited by index terms collaborative colleagues

Tools and Actions:	Request Permissions Review this Article Save this Article to a Binder Display Formats: BibTeX EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/355705.355710 What is a DOI?

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	CAVINESS, B.F., ET AL. The SAC-1 Gaussian polynomial system. Tech. Rep. in preparation, Comptr. Sci Dep, U. of Wisconsin, Madison, Wis.
	2	COLLINS, G.E. Polynomial remainder sequences and determinants. Amer. Math. Monthly 73, 7 (1966), 708-712.
	3	COLLINS, G E. Computing time analysis for some arithmetic and algebraic algorithms. Proc. 1968 Summer Inst. on Symbolic Math. Comp., IBM Federal Systems Center, 1968, pp. 195-231.
	4	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]
	5	COLLINS, G.E. Computer algebra of polynomial and rational functions. Amer. Math. Monthly 80, 7 (1973), 725-755.
	6	COLLINS, G.E. The computing time of the Euclidean algorithm. SIAM 7. Computing $, 1 (March 1974), 1-10.
	7	COLLINS, G.E. The SAC-1 list processing system. Tech. Rep. 129, Comptr. Science Dep., U. of Wisconsin, Madison, Wis., July 1971.
	8	CoLLIr~S, G.E. The SAC-1 integer arithmetic system--version III. Tech. Rep. 156, Comptr. Sci. Dep., U. of Wisconsin, Madison, Wis., July 1972.
	9	COLLINS, G.E. The SAC-1 polynomial system. Tech. Rep. 115, Comptr. Sci. Dep., U. of Wisconsin, Madison, Wis., March 1971.
	10	COLLINS, G.E. The SAC-1 rational function system. Tech. Rep. 135, Comptr. Sci. Dep., U. of Wisconsin, Madison, Wis., Sept. 1971.
	11	COLLINS, G.E. The SAC-1 polynomial GCD and resultant system. Teeh. Rep. 145, Comptr. Sci. Dep., U. of Wisconsin, Madison, Wis., Feb. 1972.
	12	COLLINS, G.E., AND HEINDEL, L.E. The SAC-I polynomial real zero system. Tech. Rep. 93, Comptr. Sci. Dep., U. of Wisconsin, Madison, Wis., Aug. 1970.
	13	COLLINS, G.E., HEINDEL, L.E., HOROWITZ, E., MCCLELLAN, M.T., XND MUSSEB, D.R. The SAC-1 modular arithmetic system. Tech. Rep. 10, Comptr. Center, U. of Wisconsin, Madison, Wis., june 1969.
	14	COLLINS, G.E., A.ND Horowitz, E. The SAC-1 partial fraction decomposition and rational function integration system. Tech. Rep. 80, Comptr. Sci. Dep., U. of Wisconsin, Madison, Wis., Feb. 1970.
	15	COLLINS, G.E., ~,ND McCLELLAN, M.T. The SAC-1 polynomial linear algebra system. Tech. Rep. 154, Comptr. Sci. Dep., U. of Wisconsin, Madison, Wis., April 1972.
	16	COLLINS, G.E., AND MUSSER, D.R. The SAC-1 polynomial factorization system. Tech. Rep. 157, Comptr. Sci. Dep., U. of Wisconsin, Madison, Wis., March 1972.
	17	COr~KWaI~HT, N.B. IntroducIion to the Theory of Equations. Ginn and Co., Boston, Mass., 1941.
	18	Lee Edward Heindel, Algorithms for exact polynomial root calculation, 1971
	19	Lee E. Heindel, Integer Arithmetic Algorithms for Polynomial Real Zero Determination, Journal of the ACM (JACM), v.18 n.4, p.533-548, Oct. 1971 [doi>10.1145/321662.321667]
	20	Donald E. Knuth, The art of computer programming, volume 1 (3rd ed.): fundamental algorithms, Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1997
	21	KNUTIt, D.E. The Art of Computer Programming, Vol. 2: Seminumerzcal Algorithms. Addison-Wesley, Reading, Mass, 1969.
	22	Loos, R.G.K. A constructive approach to algebraic numbers. To appear in SIAM J. Computing.
	23	MARDEN, M.K. The Geometry of the Zeros of a Polynomial in a Complex Variable. Amer. Math. Soc., Providence, R I., 1966.
	24	Mvss~a, D.R. Algorithms for polynomial factorization. Tech. Rep. 134 (Ph.D. Th.), Comptr. Sci. Dep. U. of Wisconsin, Madison, Wis., Sept. 1971.
	25	David R. Musser, Multivariate Polynomial Factorization, Journal of the ACM (JACM), v.22 n.2, p.291-308, April 1975 [doi>10.1145/321879.321890]
	26	James Robert Pinkert, Algebraic algorithms for computing the complex zeros of gaussian polynomials., 1973
	27	PINKERT, J.R. Algebraic algorithms for computing the complex zeros of Gaussian polynomials. Tech. Rep. 188, Comput. Sci. Dep., U. of Wisconsin, Madison, Wis., July 1973.
	28	WILF, H.S. Mathematics for the Physical Sciences. Wiley, New York, 1962.

CITED BY 4

	Achim Schweikard, Real zero isolation for trigonometric polynomials, ACM Transactions on Mathematical Software (TOMS), v.18 n.3, p.350-359, Sept. 1992
	Herbert S. Wilf, A Global Bisection Algorithm for Computing the Zeros of Polynomials in the Complex Plane, Journal of the ACM (JACM), v.25 n.3, p.415-420, July 1978
	George E. Collins , Werner Krandick, An efficient algorithm for infallible polynomial complex root isolation, Papers from the international symposium on Symbolic and algebraic computation, p.189-194, July 27-29, 1992, Berkeley, California, United States
	Calin Alexe Muresan, Comparative methods for the polynomial isolation, Proceedings of the WSEAES 13th international conference on Computers, p.634-638, July 23-25, 2009, Rodos, Greece