Complexity of Bezout’s Theorem VII: Distance Estimates in the Condition Metric

Authors:
Carlos Beltrán;Michael Shub
Affiliations:
University of Toronto, Department of Mathematics, Toronto, ON, Canada;University of Toronto, Department of Mathematics, Toronto, ON, Canada
Venue:
Foundations of Computational Mathematics
Year:
2009

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The Condition Metric in the Space of Rectangular Full Rank Matrices

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Spherical Radon transform and the average of the condition number on certain Schubert subvarieties of a Grassmannian

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Abstract

We study geometric properties of the solution variety for the problem of approximating solutions of systems of polynomial equations. We prove that given the two pairs (f i ,ζ i ), i=1,2, there exist a short path joining them such that the complexity of following the path is bounded by the logarithm of the condition number of the problems.