The structure of sparse resultant matrices

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The structure of sparse resultant matrices

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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: 189 - 196

Year of Publication: 1997

ISBN:0-89791-875-4

Authors

Ioanis Z. Emiris	INRIA, B.P. 93, Sophia-Antipolis 06902, France
Victor Y. Pan	Mathematics and Computer Science Department, CUNY, Bronx, NY

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): 4, Downloads (12 Months): 13, Citation Count: 12

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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	Dario Bini , Victor Y. Pan, Polynomial and matrix computations (vol. 1): fundamental algorithms, Birkhauser Verlag, Basel, Switzerland, 1994
	2	John F. Canny , Ioannis Z. Emiris, An Efficient Algorithm for the Sparse Mixed Resultant, Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, p.89-104, May 10-14, 1993
	3	J. F. Canny , E. Kaltofen , L. Yagati, Solving systems of nonlinear polynomial equations faster, Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation, p.121-128, July 17-19, 1989, Portland, Oregon, United States [doi>10.1145/74540.74556]
	4	John Canny , Paul Pedersen, An Algorithm for the Newton Resultant, Cornell University, Ithaca, NY, 1993
	5	Ioannis Z. Emiris, On the complexity of sparse elimination, Journal of Complexity, v.12 n.2, p.134-166, June 1996 [doi>10.1006/jcom.1996.0010]
	6	EMIms, I. A general solver based on sparse resultants: Numerical issues and kinematic applications. Tech. Rep. 3110, INRIA Sophia-Antipolis, France, Jan. 1997.
	7	Ioannis Z. Emiris , John F. Canny, Efficient incremental algorithms for the sparse resultant and the mixed volume, Journal of Symbolic Computation, v.20 n.2, p.117-149, Aug. 1995 [doi>10.1006/jsco.1995.1041]
	8	EMWdS, I., AND PAN, V. Techniques for exploiting structure in matrix formulae of the sparse resultant. Calcolo, Spec. Issue on Workshop on Toeplitz Matrices, Cortona (1997). To appear.
	9	Erich Kaltofen , Yagati N. Lakshman, Improved Sparse Multivariate Polynomial Interpolation Algorithms, Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation, p.467-474, July 04-08, 1988
	10	Erich Kaltofen , Victor Pan, Processor efficient parallel solution of linear systems over an abstract field, Proceedings of the third annual ACM symposium on Parallel algorithms and architectures, p.180-191, July 21-24, 1991, Hilton Head, South Carolina, United States [doi>10.1145/113379.113396]
	11	KAaATSUBA, A., AND OFMAN, Y. Multiplication of multidigit numbers on automata. Soviet Physics Dokl. 7 (1963), 595-596.
	12	Dinesh Manocha, Solving Systems of Polynomial Equations, IEEE Computer Graphics and Applications, v.14 n.2, p.46-55, March 1994 [doi>10.1109/38.267470]
	13	Bernard Mourrain , Victor Y. Pan, Solving special polynomial systems by using structured matrices and algebraic residues, Selected papers of a conference on Foundations of computational mathematics, p.287-304, September 1997, Rio de Janeiro, Brazil
	14	PAN, V. Numerical computation of a polynomial GCD and extensions. Tech. Rep. 2969, INRIA, Sophia- Antipolis, France, Aug. 1996.
	15	Victor Y. Pan, Parallel computation of polynomial GCD and some related parallel computations over abstract fields, Theoretical Computer Science, v.162 n.2, p.173-223, Aug. 20, 1996 [doi>10.1016/0304-3975(96)00030-8]
	16	Bernd Sturmfels, On the Newton Polytope of the Resultant, Journal of Algebraic Combinatorics: An International Journal, v.3 n.2, p.207-236, April 1994 [doi>10.1023/A:1022497624378]
	17	VAN DER WAEaDEN, B. Modern Algebra, 3rd ed. F. Ungar Publishing Co., New York, 1950.
	18	D H Wiedemann, Solving sparse linear equations over finite fields, IEEE Transactions on Information Theory, v.32 n.1, p.54-62, Jan. 1986 [doi>10.1109/TIT.1986.1057137]
	19	ZlePEL, R. Effective Polynomial Computation. Kluwer Academic Publishers, Boston, 1993.

CITED BY 12

	Ioannis Z. Emiris , Victor Y. Pan, Symbolic and numeric methods for exploiting structure in constructing resultant matrices, Journal of Symbolic Computation, v.33 n.4, p.393-413, April 2002
	Didier Bondyfalat , Bernard Mourrain , Victor Y. Pan, Controlled iterative methods for solving polynomial systems, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.252-259, August 13-15, 1998, Rostock, Germany
	John F. Canny , Ioannis Z. Emiris, A subdivision-based algorithm for the sparse resultant, Journal of the ACM (JACM), v.47 n.3, p.417-451, May 2000
	Hoon Hong , Manfred Minimair, Sparse resultant of composed polynomials I^* mixed-unmixed case, Journal of Symbolic Computation, v.33 n.4, p.447-465, April 2002
	Ioannis Z. Emiris, Computing integer points in Minkowski sums, Proceedings of the sixteenth annual symposium on Computational geometry, p.29-36, June 12-14, 2000, Clear Water Bay, Kowloon, Hong Kong
	Bernard Mourrain , Victor Y. Pan, Asymptotic acceleration of solving multivariate polynomial systems of equations, Proceedings of the thirtieth annual ACM symposium on Theory of computing, p.488-496, May 24-26, 1998, Dallas, Texas, United States
	Victor Y. Pan, Approximate polynomial Gcds, Padé approximation, polynomial zeros and bipartite graphs, Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms, p.68-77, January 25-27, 1998, San Francisco, California, United States
	Manfred Minimair, Factoring sparse resultants of linearly combined polynomials, Proceedings of the 2003 international symposium on Symbolic and algebraic computation, p.207-214, August 03-06, 2003, Philadelphia, PA, USA
	Manfred Minimair, Sparse Resultant under Vanishing Coefficients, Journal of Algebraic Combinatorics: An International Journal, v.18 n.1, p.53-73, July 2003
	Manfred Minimair, Sparse resultant of composed polynomials II unmixed--mixed case, Journal of Symbolic Computation, v.33 n.4, p.467-478, April 2002
	Manfred Minimair, Dense resultant of composed polynomials mixed-mixed case, Journal of Symbolic Computation, v.36 n.6, p.825-834, December 2003
	Manfred Minimair, Resultants of skewly composed polynomials, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy