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.
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Communicated by Felipe Cucker.
Research was partially supported by MTM2007-62799 and by an NSERC discovery grant.
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Beltrán, C., Shub, M. Complexity of Bezout’s Theorem VII: Distance Estimates in the Condition Metric. Found Comput Math 9, 179–195 (2009). https://doi.org/10.1007/s10208-007-9018-5
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DOI: https://doi.org/10.1007/s10208-007-9018-5