TY - JOUR
T1 - Computing all nonsingular solutions of cyclic-n polynomial using polyhedral homotopy continuation methods
AU - Dai, Yang
AU - Kim, Sunyoung
AU - Kojima, Masakazu
N1 - Funding Information:
Research supported by KRF 2001-015-DP0023.
PY - 2003/3/1
Y1 - 2003/3/1
N2 - 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.
AB - 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.
KW - Homotopy continuation methods
KW - Nonlinear programming
KW - Systems of equations
UR - http://www.scopus.com/inward/record.url?scp=0037334665&partnerID=8YFLogxK
U2 - 10.1016/S0377-0427(02)00698-2
DO - 10.1016/S0377-0427(02)00698-2
M3 - Article
AN - SCOPUS:0037334665
SN - 0377-0427
VL - 152
SP - 83
EP - 97
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1-2
ER -