Computing all nonsingular solutions of cyclic- n polynomial using polyhedral homotopy continuation methods
Computing all nonsingular solutions of cyclic- n polynomial using polyhedral homotopy continuation methods
复制标题
使用多面体同伦连续方法计算循环 n 多项式的所有非奇异解
DOI：
10.1016/s0377-0427(02)00698-2
复制
发表时间：
2003
影响因子：
2.4
通讯作者：
M. Kojima
中科院分区：
文献类型：
--
作者：
Yang Dai;Sunyoung Kim;M. Kojima
对于大于11的维数，循环n多项式方程的所有孤立解都是未知的。利用循环n多项式的两种对称结构，利用多面体同伦延拓方法有效地计算了方程的所有孤立非奇异解，并验证了生成的近似解的正确性.给出了循环8到循环12多项式方程的数值结果，包括它们的解信息。
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.