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Asymptotic acceleration of solving multivariate polynomial systems of equations
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Source Annual ACM Symposium on Theory of Computing archive
Proceedings of the thirtieth annual ACM symposium on Theory of computing table of contents
Dallas, Texas, United States
Pages: 488 - 496  
Year of Publication: 1998
ISBN:0-89791-962-9
Authors
Bernard Mourrain  INRIA, SAGA, BP 93, 06902 Sophia-Antipolis, France
Victor Y. Pan  Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY
Sponsor
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 3,   Downloads (12 Months): 31,   Citation Count: 8
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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, Auzlnger and H,$, Stetter. An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, In Proc. Intern. Conf. on Numerical Math., volume 86 of htt. Series of Numerical Math, pages 11-30. Blrkhauser, 1988,
 
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.I'.E Cardinal. On two iterative methods for approximating the roots of a polynomial. In J. Renegar, M. Shub, and S. Smale, editors, Proc. AMS-SIAM Summer Seminar on Math. of Numerical Analysis, (Park City, Utah, 1995), volume 32 of Lectures in Applied Math., pages 165--188. Am. Math. Soe. Press, 1996.
 
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J.P. Cardinal and B. Mourrain. Algebraic approach of residues and applications. In J. Reneger, M. Shub, and S. Smale, editors, Proc. AM$.SIAM Summer Seminar on Math. of Numerical Analysis, (Park City, Utah, 1995), volume 32 of Lectures in Applied Math., pages 189--210. Am. Math. Soc. Press, 1996.
 
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M. Elkadi and B. Mourrain. Approche Effective des R~sidus Alg6briques. Rapport de Recherche 2884, INRIA, 1996.
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I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky. Discriminants, Resultants and Multidimensional Determinants. Birkhiiuser, Boston-Basel-Berlin, 1994.
 
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D.Kapur and Y.N. Laks~an. Elimination methods: an introducton. In B. Donald, D. Kaput, and J. Mundy, editors, $ymbolic and Numerical Computation for Artifitial Intellingence, pages 45--89. Academic Press, New York, 1992.
 
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ES. Macaulay. Some formulae in elimination. Prec. London Math. 5oc., 1(33):3-27, 1902.
 
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F.S. Macaulay. The Algebraic Theory of Modular Systems. Cambridge Univ. Press, 1916.
 
14
B. Mourrain. Solving polynomial systems by matrix computations. Preprint, submitted, 1997.
 
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B. Mourrain and V. Y. Pan. Multidimensional structured matrices and polynomial systems. Calcolo, (Special Issue, Workshop on Toeplitz Matrices: Structure, Algorithms and Applications), 33:389--401, 1997.
 
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B. Mourrain and V.Y. Pan. Multivariate polynomials, duality and structured matrices. Preprint, submitted for publication, 1997.
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V.Y. Pan. Optimal and nearly optimal algorithms for appro.v,imating complex polynomial zeros. Computers and Math. Appls., 31(12):97-138, 1996.
 
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P. S. Pedersen and B. $turmfels. Product formulas for resul. tents and Chow forms. Math. Zeitschrift, 214:377-396, 1993.
 
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B.L. Van der Waerden. Modern Algebra, Vol. II. Frederick Ungar Publishing Co, 1948.

CITED BY  8

Collaborative Colleagues:
Bernard Mourrain: colleagues
Victor Y. Pan: colleagues