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 -