An Efficient Algorithm for Computing Minimal Polynomials of Polynomial Matrices

Bo Yu; Yanyan Xu

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An Efficient Algorithm for Computing Minimal Polynomials of Polynomial Matrices

Bo Yu * #,Yanyan Xu

Department of Applied Mathematics, Dalian University of Technology

*Correspondence author

#Submitted by

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Funding: none

Opened online:16 February 2005

Accepted by: none

Citation: Bo Yu,Yanyan Xu.An Efficient Algorithm for Computing Minimal Polynomials of Polynomial Matrices[OL]. [16 February 2005] http://en.paper.edu.cn/en_releasepaper/content/1554

In this paper, an efficient algorithm 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. Comparison with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.

Keywords:Minimal polynomial, polynomial matrix, algorithm

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