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

Yang Dai; Sunyoung Kim; Masakazu Kojima

doi:10.1016/S0377-0427(02)00698-2

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

Yang Dai, Sunyoung Kim, Masakazu Kojima

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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.

Original language	English
Pages (from-to)	83-97
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	152
Issue number	1-2
DOIs	https://doi.org/10.1016/S0377-0427(02)00698-2
State	Published - 1 Mar 2003

Bibliographical note

Funding Information:
Research supported by KRF 2001-015-DP0023.

Keywords

Homotopy continuation methods
Nonlinear programming
Systems of equations

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10.1016/S0377-0427(02)00698-2

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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.",

keywords = "Homotopy continuation methods, Nonlinear programming, Systems of equations",

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AU - Kojima, Masakazu

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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

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IS - 1-2

ER -

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

Abstract

Bibliographical note

Keywords

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