Generic regular decompositions for parametric polynomial systems

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• 作者：Zhenghong Chen ; Xiaoxian Tang ; Bican Xia
• 关键词：Generic regular decomposition ; parametric polynomial system ; regular ; decompositionunstable variety
• 刊名：Journal of Systems Science and Complexity
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：28
• 期：5
• 页码：1194-1211
• 全文大小：278 KB
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• 作者单位：Zhenghong Chen (1)
  Xiaoxian Tang (1)
  Bican Xia (1)
  
  1. School of Mathematical Sciences, Peking University, Beijing, 100084, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory and Control
  Applied Mathematics and Computational Methods of Engineering
  Operations Research/Decision Theory
  Probability Theory and Stochastic Processes
  
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences, co-published with Springer
• ISSN：1559-7067

文摘

This paper presents a generalization of the authors-earlier work. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in the authors-previous work for generic zero-dimensional systems, are extended to the case where the parametric systems are not necessarily zero-dimensional. An algorithm is provided to compute GRDs and the associated RDU varieties of parametric systems simultaneously on the basis of the algorithm for generic zero-dimensional systems proposed in the authors-previous work. Then the solutions of any parametric system can be represented by the solutions of finitely many regular systems and the decomposition is stable at any parameter value in the complement of the associated RDU variety of the parameter space. The related definitions and the results presented in the authors-previous work are also generalized and a further discussion on RDU varieties is given from an experimental point of view. The new algorithm has been implemented on the basis of DISCOVERER with Maple 16 and experimented with a number of benchmarks from the literature.