著者

郡司 貴之

出版者

湘南工科大学

雑誌

湘南工科大学紀要 = Memoirs of Shonan Institute of Technology (ISSN:09192549)

巻号頁・発行日

vol.42, no.1, pp.71-84, 2008-03-18

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A system of multi variables polynomial equations arises in many fields of science and engineering. The polyhedralhomotopy continuation method is one of the methods for finding all isolated complex solutions of systems of polynomialequations. First, the method constructs the homotopy systems adding the parameter for the systems of polynomial equations.Next, it finds the solutions of starting systems of them. It traces the homotopy curves which can be defined as oneof the solution set of homotopy systems from the solutions of starting system. As a result of tracing, the method givesthe solutions of system of polynomial equations.We implemented the software PHoM (a Polyhedral HOmotopy continuation Method for polynomial systems) whichcan automatically enumerate all isolated solutions by polyhedral homotopy continuation method, including constructionof the homotopy systems, tracing the homotopy curve and verification of the obtained solutions. In numerical experiment,we show efficient of the software.A system of polynomial equations of increasing size have an increasing number of the homotopy curves. The softwareusing single CPU has been limited the size of problems. For solving large size problems, we consider parallel computationof the polyhedral homotopy continuation method. We implemented parallelization through all stages of themethod as PHoMpara (PARAllel implementation of the Polyhedral HOmotopy continuation Method for polynomial systems).The software PHoMpara uses Ninf-1 and PC cluster as parallel computer environment. Furthermore, we proposeimproving efficiency of parallelization. Specially, we indicate a weak point of existing parallel calculation of mixed volumeand we suggest improving calculation of it. In numerical experiments, we show effect of the proposed parallel techniques.And we present that can enumerate all isolated solutions of the problems that had not been solved.A system of multi variables polynomial equations arises in many fields of science and engineering. The polyhedralhomotopy continuation method is one of the methods for finding all isolated complex solutions of systems of polynomialequations. First, the method constructs the homotopy systems adding the parameter for the systems of polynomial equations.Next, it finds the solutions of starting systems of them. It traces the homotopy curves which can be defined as oneof the solution set of homotopy systems from the solutions of starting system. As a result of tracing, the method givesthe solutions of system of polynomial equations.We implemented the software PHoM (a Polyhedral HOmotopy continuation Method for polynomial systems) whichcan automatically enumerate all isolated solutions by polyhedral homotopy continuation method, including constructionof the homotopy systems, tracing the homotopy curve and verification of the obtained solutions. In numerical experiment,we show efficient of the software.A system of polynomial equations of increasing size have an increasing number of the homotopy curves. The softwareusing single CPU has been limited the size of problems. For solving large size problems, we consider parallel computationof the polyhedral homotopy continuation method. We implemented parallelization through all stages of themethod as PHoMpara (PARAllel implementation of the Polyhedral HOmotopy continuation Method for polynomial systems).The software PHoMpara uses Ninf-1 and PC cluster as parallel computer environment. Furthermore, we proposeimproving efficiency of parallelization. Specially, we indicate a weak point of existing parallel calculation of mixed volumeand we suggest improving calculation of it. In numerical experiments, we show effect of the proposed parallel techniques.And we present that can enumerate all isolated solutions of the problems that had not been solved.