homotopy continuation methods

PHoM – a Polyhedral Homotopy Continuation Method for Polynomial Systems

  • Katsuki Fujisawa
  • Sunyoung Kim
  • Masakazu Kojima
  • Tomohiko Mizutani
  • Takayuki Gunji
  • Akiko Takeda
    • Categories Nonlinear Systems and Least-Squares Tags , , , ,

    PHoM is a software package in C++ for finding all isolated solutions of polynomial systems using a polyhedral homotopy continuation method. Among three modules constituting the package, the first module StartSystem constructs a family of polyhedral-linear homotopy functions, based on the polyhedral homotopy theory, from input data for a given system of polynomial equations $\f(\x) … Read more

    Computing All Nonsingular Solutions of Cyclic-n Polynomial Using Polyhedral Homotopy Continuation Methods

  • Yang Dai
  • Sunyoung Kim
  • Masakazu Kojima
    • Categories Other Topics Tags , , , ,

    All isolated solutions of the cyclic-n polynomial equations are not known for larger dimensions than 11. We exploit two types of symmetric structures in the cyclic-n polynomial to compute all isolated nonsingular solutions of the equations efficiently by the polyhedral homotopy continuation method and to verify the correctness of the generated approximate solutions. Numerical results … Read more