Probabilistic Condition Number Estimates for Real Polynomial Systems I: A Broader Family of Distributions Academic Article uri icon


  • 2018, SFoCM. We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particularfor a version of the condition number defined by Cucker and used later by Cucker, Krick, Malajovich, and Wscheborwe establish new probabilistic estimates that allow a much broader family of measures than considered earlier. We also generalize further by allowing overdetermined systems. In Part II, we study smoothed complexity and how sparsity (in the sense of restricting which terms can appear) can help further improve earlier condition number estimates.

published proceedings


altmetric score

  • 0.25

author list (cited authors)

  • Erguer, A. A., Paouris, G., & Rojas, J. M.

citation count

  • 14

complete list of authors

  • Erguer, Alperen A||Paouris, Grigoris||Rojas, J Maurice

publication date

  • February 2019