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Computing the Frobenius Normal Form of a Sparse Matrix

In: Computer Algebra in Scientific Computing

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  • Gilles Villard

    (CNRS-LMC)

Abstract

We probabilistically determine the Frobenius form and thus the characteristic polynomial of a matrix $$A \in {^{n \times n}}$$ by O(μnlog(n)) multiplications of A by vectors and 0 (μn2 log2 (n)loglog(n)) arithmetic operations in the field F . The parameter μ.L is the number of distinct invariant factors of A, it is less than $$3{{\sqrt n } \mathord{\left/ {\vphantom {{\sqrt n } 2}} \right. \kern-\nulldelimiterspace} 2}$$ in the worst case. The method requires O(n) storage space in addition to that needed for the matrix A.

Suggested Citation

  • Gilles Villard, 2000. "Computing the Frobenius Normal Form of a Sparse Matrix," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing, pages 395-407, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57201-2_30
    DOI: 10.1007/978-3-642-57201-2_30
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