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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A condition number theorem for underdetermined polynomial systems


Author: Jérôme Dégot
Journal: Math. Comp. 70 (2001), 329-335
MSC (2000): Primary 65H10
Published electronically: July 10, 2000
MathSciNet review: 1458220
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Abstract:

The condition number of a numerical problem measures the sensitivity of the answer to small changes in the input. In their study of the complexity of Bézout's theorem, M. Shub and S. Smale prove that the condition number of a polynomial system is equal to the inverse of the distance from this polynomial system to the nearest ill-conditioned one. Here we explain how this result can be extended to underdetermined systems of polynomials (that is with less equations than unknowns).


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Additional Information

Jérôme Dégot
Affiliation: Lycée Fénelon, 2, rue de l’éperon, 75006 Paris, France
Email: jerome.degot@wanadoo.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-00-00934-0
PII: S 0025-5718(00)00934-0
Received by editor(s): August 13, 1996
Published electronically: July 10, 2000
Article copyright: © Copyright 2000 American Mathematical Society