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

abstract

• 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.

authors

• Paouris, Grigoris
• Rojas, Joseph

published proceedings

• FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

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

publisher

• Springer Nature  Publisher

published in

• Foundations of Computational Mathematics  Journal

keywords

• Condition Number
• Epsilon Net
• Kappa
• Overdetermined
• Probabilistic Bound
• Real-solving
• Subgaussian

Digital Object Identifier (DOI)

• 10.1007/s10208-018-9380-5

start page

• 131

end page

• 157

volume

• 19

issue

• 1

URL

• http://dx.doi.org/10.1007/s10208-018-9380-5