Gröbner bases and matrix eigenproblems

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Gröbner bases and matrix eigenproblems

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

Pages: 26 - 32

Year of Publication: 1996

ISSN:0163-5824

Author

Robert M. Corless

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 11, Downloads (12 Months): 37, Citation Count: 5

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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] A.-M. E. Allison & R. M. Corless, "Bifurcation Study of a model of Flow-Induced Vibration, part II", in preparation.
	2	[2] W. Auzinger and H. J. Stetter, "An Elimination Algorithm for the Computation of All Zeros of a System of Multivariate Polynomial Equations", Numerical Mathematics Singapore 1988, Ravi P. Agarwal, Y. M. Chow, & S. J. Wilson, eds, ISNM vol. 86, Birkhäuser, pp. 11-30, 1988.
	3	Angelika Bunse-Gerstner , Ralph Byers , Volker Mehrmann, Numerical methods for simultaneous diagonalization, SIAM Journal on Matrix Analysis and Applications, v.14 n.4, p.927-949, Oct. 1993 [doi>10.1137/0614062]
	4	[4] David Cox, John Little, & Donal O'Shea, Ideals, Varieties, and Algorithms, Springer-Verlag, 1992.
	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	[6] Robert M. Corless, Patrizia M. Gianni, Barry M. Trager, "Schur form and generic combinations for multiple roots", in progress.
	7	[7] J. W. Demmel & Bo Kågström, "Computing Stable Eigendecompositions of Matrix Pencils", Linear Algebra and its Applications, Volume 88/89, pp. 139- 186, 1987.
	8	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]
	9	[9] L. Gonzalez-Vega, "Some examples of problem solving by using the symbolic viewpoint when dealing with polynomial systems of equations" In: Computer Algebra in Science and Engineering (editors J. Fleischer, J. Grabmeier, F. W. Hehl and W. Küchlin), World Scientific, pp. 102-116, 1995.
	10	[10] L. Gonzalez-Vega, "Symbolic Recipes for Polynomial System Solving: Real Solutions", notes for ISSAC '96 tutorial.
	11	[11] Nathan Jacobson, Basic Algebra, 2nd edition, W. H. Freeman, 1989.
	12	[12] Roger Horn & Charles Johnson, Matrix Analysis, Cambridge University Press, 1985 (1991 printing used here).
	13	Dinesh Manocha , Shankar Krishnan, Solving algebraic systems using matrix computations, ACM SIGSAM Bulletin, v.30 n.4, p.4-21, Dec. 1996 [doi>10.1145/242961.242965]
	14	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]
	15	[15] Hans J. Stetter, "Multivariate Polynomial Equations as Matrix Eigenproblems", In: Contributions to Numerical Mathematics, World Scientific Series in Applicable Analysis, Volume 2, pp. 355-371, 1993.
	16	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 5

	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
	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
	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
	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
	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