KhovanskiiRolle Continuation for Real Solutions Academic Article uri icon

abstract

  • We present a new continuation algorithm to find all real solutions to a nondegenerate system of polynomial equations. Unlike homotopy methods, the algorithm is not based on a deformation of the system; instead, it traces real curves connecting the solutions to one system of equations to those of another, eventually leading to the desired real solutions. It also differs from homotopy methods in that it follows only real paths and computes no complex solutions to the original equations. The number of curves traced is essentially bounded above by the fewnomial bound for real solutions, and the method takes advantage of any slack in that bound. 2011 SFoCM.

published proceedings

  • Foundations of Computational Mathematics

author list (cited authors)

  • Bates, D. J., & Sottile, F.

citation count

  • 13

complete list of authors

  • Bates, Daniel J||Sottile, Frank

publication date

  • October 2011