Computing the Frobenius Normal Form of a Sparse Matrix

Gilles Villard
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Gilles Villard: CNRS-LMC

A chapter in Computer Algebra in Scientific Computing, 2000, pp 395-407 from Springer

Abstract: 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.

Keywords: Normal Form; Arithmetic Operation; Characteristic Polynomial; Binary Search; Minimum Polynomial (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57201-2_30

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DOI: 10.1007/978-3-642-57201-2_30

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