Numerical stability of path tracing in polyhedral homotopy continuation methods

Sunyoung Kim, Masakazu Kojima

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The reliability of polyhedral homotopy continuation methods for solving a polynomial system becomes increasingly important as the dimension of the polynomial system increases. High powers of the homotopy continuation parameter t and ill-conditioned Jacobian matrices encountered in tracing of homotopy paths affect the numerical stability. We present modified homotopy functions with a new homotopy continuation parameter s and various scaling strategies to enhance the numerical stability. Advantages of employing the new homotopy parameter 5 are discussed. Numerical results are included to illustrate the improved performance of the presented techniques.

Original languageEnglish
Pages (from-to)329-348
Number of pages20
JournalComputing (Vienna/New York)
Issue number4
StatePublished - Nov 2004


  • Numerical stability
  • Path tracing
  • Polyhedral homotopy continuation methods
  • Polynomial system


Dive into the research topics of 'Numerical stability of path tracing in polyhedral homotopy continuation methods'. Together they form a unique fingerprint.

Cite this