A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots

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A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots

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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: 133 - 140

Year of Publication: 1997

ISBN:0-89791-875-4

Authors

Robert M. Corless	Department of Applied Mathematics, University of Western Ontario, London, Canada N6A 5B7
Patrizia M. Gianni	Department of Mathematics, University of Pisa, 56127 Pisa, Italy
Barry M. Trager	IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York

Sponsors

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

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ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 28, Citation Count: 20

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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.

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	2	AUZINGER, W., AND STETTER, H. J. An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, in Numerical Mathematics (1988), R. P. Agarwal, Y. M. Chow, and S. J. Wilson, Eds., vol. 86 of ISNM, Birkh/iuser, pp. 11-30.
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	4	Robert M. Corless, Gro¨bner bases and matrix eigenproblems, ACM SIGSAM Bulletin, v.30 n.4, p.26-32, Dec. 1996 [doi>10.1145/242961.242968]
	5	Robert M. Corless , Patrizia M. Gianni , Barry M. Trager , Stephen M. Watt, The singular value decomposition for polynomial systems, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.195-207, July 10-12, 1995, Montreal, Quebec, Canada [doi>10.1145/220346.220371]
	6	J. C. Faugère , P. Gianni , D. Lazard , T. Mora, Efficient computation of zero-dimensional Gro¨bner bases by change of ordering, Journal of Symbolic Computation, v.16 n.4, p.329-344, Oct. 1993 [doi>10.1006/jsco.1993.1051]
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	8	T. E. Hull , R. Mathon, The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence, ACM Transactions on Mathematical Software (TOMS), v.22 n.3, p.261-280, Sept. 1996 [doi>10.1145/232826.232830]
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	11	H. Michael Möller , Hans J. Stetter, Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems, Numerische Mathematik, v.70 n.3, p.311-329, May 1995 [doi>10.1007/s002110050122]
	12	Hans J. Stetter, Analysis of zero clusters in multivariate polynomial systems, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.127-136, July 24-26, 1996, Zurich, Switzerland [doi>10.1145/236869.236919]
	13	Hans J. Stetter, Matrix eigenproblems are at the heart of polynomial system solving, ACM SIGSAM Bulletin, v.30 n.4, p.22-25, Dec. 1996 [doi>10.1145/242961.242966]

CITED BY 20

	Schuichi Moritsugu , Kazuko Kuriyama, On multiple zeros of systems of algebraic equations, Proceedings of the 1999 international symposium on Symbolic and algebraic computation, p.23-30, July 28-31, 1999, Vancouver, British Columbia, Canada
	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
	H. Michael Möller , Ralf Tenberg, Multivariate polynomial system solving using intersections of Eigenspaces, Journal of Symbolic Computation, v.32 n.5, p.513-531, November 2001
	Robert M. Corless , Mark W. Giesbrecht , Mark van Hoeij , Ilias S. Kotsireas , Stephen M. Watt, Towards factoring bivariate approximate polynomials, Proceedings of the 2001 international symposium on Symbolic and algebraic computation, p.85-92, July 2001, London, Ontario, Canada
	Didier Henrion , Jean-Bernard Lasserre, GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi, ACM Transactions on Mathematical Software (TOMS), v.29 n.2, p.165-194, June 2003
	Greg Reid , Jianliang Tang , Lihong Zhi, A complete symbolic-numeric linear method for camera pose determination, Proceedings of the 2003 international symposium on Symbolic and algebraic computation, p.215-223, August 03-06, 2003, Philadelphia, PA, USA
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	Aaron Wallack , Ioannis Z. Emiris , Dinesh Manocha, MARS: a MAPLE/MATLAB/C resultant-based solver, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.244-251, August 13-15, 1998, Rostock, Germany
	Bernard Mourrain , Jean-Pierre Técourt , Monique Teillaud, On the computation of an arrangement of quadrics in 3D, Computational Geometry: Theory and Applications, v.30 n.2, p.145-164, February 2005
	Barry H. Dayton , Zhonggang Zeng, Computing the multiplicity structure in solving polynomial systems, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.116-123, July 24-27, 2005, Beijing, China
	Bernard Mourrain, Generalized normal forms and polynomial system solving, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.253-260, July 24-27, 2005, Beijing, China
	Itnuit Janovitz-Freireich , Lajos Rónyai , Ágnes Szántó, Approximate radical of ideals with clusters of roots, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy
	Robert M. Corless , Stephen M. Watt, Report on the SNAP minisymposium at SIAM '98, ACM SIGSAM Bulletin, v.32 n.2, p.35-37, June 1998
	Xiaoli Wu , Lihong Zhi, Computing the multiplicity structure from geometric involutive form, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, July 20-23, 2008, Linz/Hagenberg, Austria
	Bin Li , Jiawang Nie , Lihong Zhi, Approximate GCDs of polynomials and sparse SOS relaxations, Theoretical Computer Science, v.409 n.2, p.200-210, December, 2008
	Bernard Mourrain , Philippe Trébuchet, Stable normal forms for polynomial system solving, Theoretical Computer Science, v.409 n.2, p.229-240, December, 2008
	Jean B. Lasserre , Monique Laurent , Philipp Rostalski, A prolongation-projection algorithm for computing the finite real variety of an ideal, Theoretical Computer Science, v.410 n.27-29, p.2685-2700, June, 2009
	Robert M. Corless , Karin Gatermann , Ilias S. Kotsireas, Using symmetries in the eigenvalue method for polynomial systems, Journal of Symbolic Computation, v.44 n.11, p.1536-1550, November, 2009
	Stef Graillat , Philippe Trébuchet, A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, July 28-31, 2009, Seoul, Republic of Korea