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论文类型：期刊论文

发表时间：2015-02-01

发表刊物：JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY

收录刊物：SCIE、EI、CSCD、Scopus

卷号：28

期号：1

页面范围：190-209

ISSN号：1009-6124

关键字：Characteristic polynomial; minimal polynomial; polynomial matrix

摘要：In this paper, a randomized Cayley-Hamilton theorem based method (abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented. It determines the coefficient polynomials term by term from lower to higher degree. By using a random vector and randomly shifting, it requires no condition on the input matrix and works with probability one. In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation, by using the modular technique, a parallelized version of the RCH method is also given. Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.