Year: 2012
Type: preprint
Abstract: Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm, which is based on the theories of subresultant chains. Furthermore, the algorithm can be naturally adopted to compute a non-redundant Wu's decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 15 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm.
Source: arXiv (Cornell University)
Authors: Tang, Xiaoxian, Chen, Zhenghong, Xia, Bican
Institution: Peking University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953092739