A note about the average number of real roots of a Bernstein polynomial system

  • Authors:
  • Diego Armentano;Jean-Pierre Dedieu

  • Affiliations:
  • Institut de Mathématiques, Université Paul Sabatier, 31062 Toulouse cedex 09, France;Institut de Mathématiques, Université Paul Sabatier, 31062 Toulouse cedex 09, France

  • Venue:
  • Journal of Complexity
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

We prove that the real roots of normal random homogeneous polynomial systems with n+1 variables and given degrees are, in some sense, equidistributed in the projective space P(R^n^+^1). From this fact we compute the average number of real roots of normal random polynomial systems given in the Bernstein basis.