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Controlled iterative methods for solving polynomial systems

Authors:

Didier Bondyfalat,

Bernard Mourrain,

Victor Y. PanAuthors Info & Claims

ISSAC '98: Proceedings of the 1998 international symposium on Symbolic and algebraic computation

Pages 252 - 259

https://doi.org/10.1145/281508.281629

Published: 01 August 1998 Publication History

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References

[1]

AUZINGER, W., AND STETTER, H. An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations. In Proc. Intern. Conf. on Numerical Math. (1988), vol. 86 of Int. Series of Numerical Math., Birkh/iuser, pp. 11-30.]]

[2]

BINI, D., AND PAN, V. Polynomial and Matrix Cornputations, Vol. 1 : Fundamental Algorithms. Birkh/iuser, Boston, 1994.]]

Digital Library

[3]

CANNY, J., AND EMIRIS, I. An efficient algorithm for the sparse mixed resultant. In Proc. Intern. Syrnp. Applied Algebra, Algebraic Algor. and Error- Corr. Codes (Puerto Rico) (1993), G. Cohen, T. Mora, and O. Moreno, Eds., vol. 263 of Lect. Notes in Cornp. Science, Springer, pp. 89-104.]]

[4]

CANNY, J., KALTOFEN, E., AND LAKSHMAN, Y. Solving Systems of Non-linear Polynomial Equations Faster. In Proc. Intern. Syrnp. Symbolic and Algebraic Cornputation (ISSAC'89) (1989), ACM Press, New York, pp. 121-128.]]

[5]

CORLESS, 1~., GIANNI, P., AND TRAGER, B. A reordered Schur factorization method for zerodimensional polynomial systems with multiple roots. In Proc. Intern. Syrnp. Symbolic and Algebraic Cornputation (ISSAC'97) (1997) ACM Press, New York, pp. 133-140.]]

[6]

Cox, D., LITTLE, J., AND O'SHEA, D. Ideals, Varieties, and Algorithms: An Introduction to Cornputational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics. Springer, 1992.]]

Digital Library

[7]

EMIRIS, I., AND PAN, V. The structure of sparse resultant matrices. In Proc. Intern. Syrnp. Symbolic and Algebraic Computation (ISSA C'97) (1997) ACM Press, New York, pp. 189-196.]]

[8]

EMIRIS, I., AND REGE, A. Monomial bases and polynomial system solving. In Proc. Intern. Syrnp. on Syrnbolic and Algebraic Computation (ISSAC'94) (1994), ACM Press, New York, pp. 114-122.]]

[9]

EMSALEM, J. G6om6trie des points 6pais. Bull. Soc. Math. France 106 (1978), 399-416.]]

[10]

FAUGERAS, O. Three-dimensional computer vision : a geometric viewpoint, vol. XXXII. Cambridge, MA ; London: MIT Press, 1993.]]

Digital Library

[11]

GELFAND, I., KAPRANOV, M., AND ZELEVINSKY, A. Discrirninants, Resultants and Multidimensional Deterrninants. Birkh/iuser, Boston-Basel-Berlin, 1994.]]

[12]

GIANNI, P., AND TRAGER, B. Computations with approximate ideals. Preprint, SNAP'96, 1997.]]

[13]

GIUSTI, M., AND HEINTZ, J. La d6termination des points isol6s et de la dimension d'une vari6t6 algebrique peut se faire en temps polynomial. In Proc. Intern. Meeting on Commutative Algebra (Cortona, 1991), vol. XXXIV of Syrnp. Mathernatica, pp. 216-255.]]

[14]

GOLUB, G. H., AND VAN LOAN, C. F. Matrix Cornputations, Johns Hopkins Univ. Press, Baltimore, Maryland (1996) (third edition).]]

[15]

LAZARD, D. R~solution des syst~mes d'~quations alg~briques. Theor. Cornp. Science 15 (1981), 77-110.]]

[16]

MACAULAY, F. Some formulae in elimination. Proc. London Math. Soc. 1, 33 (1902), 3-27.]]

[17]

MANOCHA, D. Computing selected solutions of polynomial equations. In Proc. Intern. Syrnp. Symbolic and Algebraic Computation (ISSAC'94) (1994), ACM Press, New York, pp. 1-8.]]

[18]

MANOCHA, D., AND CANNY, J. Multidimensional resultant algorithms. J. Symbolic Computation 15 (1993), 99-122.]]

Digital Library

[19]

MARINARI, M., MORA, T., AND MOLLER, H. GrSbner duality and multiplicities in polynomial system solving. In Proc. Intern. Syrnp. Symbolic and Algebraic Computation (ISSAC'95) (1995), ACM Press, New York, pp. 167-179.]]

[20]

MOUaaAIN, B. Isolated points, duality and residues. J. Pure Applied Algebra. Special Issue on Algorithms for Algebra 117 ~ 118 (May 1997), 469-494.]]

[21]

MOURRAIN, B. Solving polynomial systems by matrix computations. Manuscript. INRIA Sophia-Antipolis, France. Submitted for publication, 1997.]]

[22]

MOURRAIN, B., AND PAN, V. Multivariate polynomials, duality and structured matrices, submitted, 1997.]]

[23]

MOURRAIN, B., AND PAN, V. Y. Multidimensional structured matrices and polynomial systems. Calcolo, Special Issue, workshop on Toeplitz matrices: Structure, Algorithms and Applications 33 (1996), 389-401.]]

[24]

MOURRAIN, B., AND PAN, V. Y. Solving special polynomial systems by using structured matrices and algebraic residues. In Proc. of the Workshop on Foundations of Cornp. Math. (Rio de Janeiro, 1997) (1997), F. Cucker and M. Shub, Eds., Springer, pp. 287-304.]]

Digital Library

[25]

MOURRAIN, B., AND PAN, V. Y. Asymptotic acceleration of solving polynomial systems, 30th Ann. Syrnp. on Theory of Computing (1998) ACM Press, New York.]]

Digital Library

[26]

PEDERSEN, P. S., AND STURMFELS, B. Mixed monomial basis. In Effective Methods in Algebraic Geornetry (MEGA'9~) (Santander (Spain), 1994), vol. 143 of Progress in Math., Birkh/iuser, pp. 285-306.]]

[27]

RENEGAR, J. On the worst-case arithmetic complexity of approximating zeros of system of polynomials. SIAM J. on Computing 18 (1989), 350-370.]]

Digital Library

[28]

SAAD, Y. Iterative methods for sparse linear systems. PWS series in Computer Science. PWS, 1996.]]

Digital Library

[29]

STETTER, g. J. Eigenproblems are at the Heart of Polynomial System Solving. SIGSAM Bulletin 30, 4 (1996) ACM Press, New York, 22-25.]]

Digital Library

[30]

STURMFELS, B. Sparse elimination theory. In Cornputational Algebraic Geometry and Commutative Algebra (1993), D. Eisenbud and L. Robianno, Eds., Cambridge Univ. Press, pp. 264-298. (Proc. Cortona, June 1991).]]

[31]

VAN DER WAERDEN, B. Modern algebra, Vol. II. Frederick Ungar Publishing Co., 1948.]]

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cover image ACM Conferences

ISSAC '98: Proceedings of the 1998 international symposium on Symbolic and algebraic computation

August 1998

330 pages

ISBN:1581130023

DOI:10.1145/281508

Copyright © 1998 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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

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New York, NY, United States

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Published: 01 August 1998

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ISSAC98: International Symposium on Symbolic and Algebraic Computation

August 13 - 15, 1998

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https://dl.acm.org/doi/10.1016/j.cam.2016.08.037
Ruatta OSciabica MSzanto A(2015)Overdetermined Weierstrass iteration and the nearest consistent systemTheoretical Computer Science10.1016/j.tcs.2014.10.008562:C(346-364)Online publication date: 11-Jan-2015
https://dl.acm.org/doi/10.1016/j.tcs.2014.10.008
Khashan HSyam M(2011)QR-algebraic method for approximating zeros of system of polynomialsInternational Journal of Computer Mathematics10.1080/0020716090320172488:1(110-120)Online publication date: Jan-2011
https://doi.org/10.1080/00207160903201724
Emiris IPan VTsigaridas E(2010)Algebraic and numerical algorithmsAlgorithms and theory of computation handbook10.5555/1882757.1882774(17-17)Online publication date: 1-Feb-2010
https://dl.acm.org/doi/10.5555/1882757.1882774
Chen XYong JZheng GPaul JSun J(2006)Computing minimum distance between two implicit algebraic surfacesComputer-Aided Design10.1016/j.cad.2006.04.01238:10(1053-1061)Online publication date: 1-Oct-2006
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Mourrain BTrebuchet P(2000)Solving projective complete intersection fasterProceedings of the 2000 international symposium on Symbolic and algebraic computation10.1145/345542.345642(234-241)Online publication date: 1-Jul-2000
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Busé LElkadi MMourrain B(2000)Generalized Resultants over Unirational Algebraic VarietiesJournal of Symbolic Computation10.1006/jsco.1999.030429:4-5(515-526)Online publication date: May-2000
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