Computing all nonsingular solutions of cyclic-n polynomial using polyhedral homotopy continuation methods

Authors:
Yang Dai;Sunyoung Kim;Masakazu Kojima
Affiliations:
Bioengineering Department, University of Illinois at Chicago, 851 S. Morgan Street, Room 233 Chicago, IL;Department of Mathematics, Ewha Women's University, 11-1 Dahyun-dong, Sudaemoon-gu, Seoul 120-750, South Korea;Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro, Tokyo 152-8552 Japan
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Year:
2003

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Abstract

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 on the cyclic-8 to the cyclic-12 polynomial equations, including their solution information, are given.