Computing Minimal Polynomials of Matrices

Cheryl Praeger, M. Neunhoffer

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    We present and analyse a Monte-Carlo algorithm to computethe minimal polynomial of an n × n matrix over a finite fieldthat requires O(n3) field operations and O(n) random vectors,and is well suited for successful practical implementation.The algorithm, and its complexity analysis, use standard algorithmsfor polynomial and matrix operations. We comparefeatures of the algorithm with several other algorithms in theliterature. In addition we present a deterministic verificationprocedure which is similarly efficient in most cases but has aworst-case complexity of O(n4). Finally, we report the resultsof practical experiments with an implementation of our algorithmsin comparison with the current algorithms in the GAPlibrary.
    Original languageEnglish
    Pages (from-to)252-279
    JournalLMS Journal of Computation and Mathematics
    Volume11
    Publication statusPublished - 2008

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