Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods
We present an algorithm that computes the singular points of projective plane algebraic curves and determines their multiplicities and characters. The feasibility of the algorithm is analyzed. We prove that the algorithm has the polynomial time complexity on the degree of the algebraic curve. The al...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/230847 |
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| _version_ | 1832552115038322688 |
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| author | Zhongxuan Luo Erbao Feng Jielin Zhang |
| author_facet | Zhongxuan Luo Erbao Feng Jielin Zhang |
| author_sort | Zhongxuan Luo |
| collection | DOAJ |
| description | We present an algorithm that computes the singular points of projective plane algebraic curves and determines their multiplicities and characters. The feasibility of the algorithm is analyzed. We prove that the algorithm has the polynomial time complexity on the degree of the algebraic curve. The algorithm involves the combined applications of homotopy continuation
methods and a method of root computation of univariate polynomials. Numerical experiments show that our algorithm is feasible and efficient. |
| format | Article |
| id | doaj-art-3e11249704d84b958a3f76de3eba38d6 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3e11249704d84b958a3f76de3eba38d62025-02-03T05:59:30ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/230847230847Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation MethodsZhongxuan Luo0Erbao Feng1Jielin Zhang2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaWe present an algorithm that computes the singular points of projective plane algebraic curves and determines their multiplicities and characters. The feasibility of the algorithm is analyzed. We prove that the algorithm has the polynomial time complexity on the degree of the algebraic curve. The algorithm involves the combined applications of homotopy continuation methods and a method of root computation of univariate polynomials. Numerical experiments show that our algorithm is feasible and efficient.http://dx.doi.org/10.1155/2014/230847 |
| spellingShingle | Zhongxuan Luo Erbao Feng Jielin Zhang Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods Discrete Dynamics in Nature and Society |
| title | Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods |
| title_full | Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods |
| title_fullStr | Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods |
| title_full_unstemmed | Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods |
| title_short | Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods |
| title_sort | computing singular points of projective plane algebraic curves by homotopy continuation methods |
| url | http://dx.doi.org/10.1155/2014/230847 |
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