Matrix eigenproblems are at the heart of polynomial system solving

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Matrix eigenproblems are at the heart of polynomial system solving

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ACM SIGSAM Bulletin archive
Volume 30 , Issue 4 (December 1996) table of contents

Pages: 22 - 25

Year of Publication: 1996

ISSN:0163-5824

Author

Hans J. Stetter

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 7, Downloads (12 Months): 28, Citation Count: 11

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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	[1] W. Auzinger, H.J. Stetter: An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, in: Intern. Series in Numer. Math. (Birkhäuser) vol. 86, 11-30, 1988.
	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	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]
	4	[4] D. Lazard: Résolution des systèmes d'équations algébriques, Theor. Comp. Sci 15, 77-110, 1981.
	5	[5] M.G. Marinari, H.M. Moeller, T. Mora: Groebner duality and multiplicities in polynomial system solving , to appear in Trans. AMS.
	6	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]
	7	[7] H.J. Stetter: Multivariate polynomial equations as matrix eigenproblems, in: Series in Applicable Analysis (World Scientific) vol. 2, 355-371, 1993.

CITED BY 11

	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
	Hans J. Stetter, Stabilization of polynomial systems solving with Groebner bases, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.117-124, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Robert M. Corless , Patrizia M. Gianni , Barry M. Trager, A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.133-140, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Victor Y. Pan , Zhao Q. Chen, The complexity of the matrix eigenproblem, Proceedings of the thirty-first annual ACM symposium on Theory of computing, p.507-516, May 01-04, 1999, Atlanta, Georgia, United States
	Hans J. Stetter , Günther H. Thallinger, Singular systems of polynomials, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.9-16, August 13-15, 1998, Rostock, Germany
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	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 Hanzon , Dorina Jibetean, Global Minimization of a Multivariate Polynomial using Matrix Methods, Journal of Global Optimization, v.27 n.1, p.1-23, September 2003
	Robert M. Corless, Gröbner bases and matrix eigenproblems, ACM SIGSAM Bulletin, v.30 n.4, p.26-32, Dec. 1996
	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