Indexed by:期刊论文

Date of Publication:2015-02-01

Journal:JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY

Included Journals:SCIE、EI、CSCD、Scopus

Volume:28

Issue:1

Page Number:190-209

ISSN No.:1009-6124

Key Words:Characteristic polynomial; minimal polynomial; polynomial matrix

Abstract: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.