Corpus ID: 52188085

Probabilistic Condition Number Estimates for Real Polynomial Systems II: Structure and Smoothed Analysis

  title={Probabilistic Condition Number Estimates for Real Polynomial Systems II: Structure and Smoothed Analysis},
  author={A. A. Erg{\"u}r and G. Paouris and J. M. Rojas},
  • A. A. Ergür, G. Paouris, J. M. Rojas
  • Published 2018
  • Mathematics, Computer Science
  • ArXiv
  • We consider the sensitivity of real zeros of polynomial systems with respect to perturbation of the coefficients, and extend our earlier probabilistic estimates for the condition number in two directions: (1) We give refined bounds for the condition number of random structured polynomial systems, depending on a variant of sparsity and an intrinsic geometric quantity called dispersion. (2) Given any structured polynomial system $P$, we prove the existence of a nearby well-conditioned structured… CONTINUE READING
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