Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems Academic Article uri icon


  • Smales -theory uses estimates related to the convergence of Newtons method to certify that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified implements algorithms based on -theory to certify solutions of polynomial systems using both exact rational arithmetic and arbitrary precision floating point arithmetic. It also implements algorithms that certify whether a given point corresponds to a real solution, and algorithms to heuristically validate solutions to overdetermined systems. Examples are presented to demonstrate the algorithms.

published proceedings

  • ACM Transactions on Mathematical Software

altmetric score

  • 8.024

author list (cited authors)

  • Hauenstein, J. D., & Sottile, F.

citation count

  • 84

complete list of authors

  • Hauenstein, Jonathan D||Sottile, Frank

publication date

  • August 2012