Abstract.
We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those having multiple real zeros). As a consequence, a smoothed analysis of this condition number follows.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
To Steve, on his 80th birthday, with admiration and esteem
Rights and permissions
About this article
Cite this article
Cucker, F., Krick, T., Malajovich, G. et al. A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis. J. Fixed Point Theory Appl. 6, 285–294 (2009). https://doi.org/10.1007/s11784-009-0127-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11784-009-0127-4