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The RCH method for computing minimal polynomials of polynomial matrices

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Bo Yu & Yanyan Xu

  2. School of Science, Dalian University of Technology, Panjin, 124221, China

    Jintao Zhang

Authors
  1. Bo Yu
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  2. Jintao Zhang
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  3. Yanyan Xu
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Corresponding author

Correspondence to Bo Yu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11171051, the Major Research plan of the National Natural Science Foundation of China under Grant No. 91230103 and the Fundamental Research Funds for the Central Universities under Grant No. DUT14RC(3)023.

This paper was recommended for publication by Editor GAO Xiao-Shan.

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Yu, B., Zhang, J. & Xu, Y. The RCH method for computing minimal polynomials of polynomial matrices. J Syst Sci Complex 28, 190–209 (2015). https://doi.org/10.1007/s11424-014-2256-0

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  • DOI: https://doi.org/10.1007/s11424-014-2256-0

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