On the computation of minimal polynomials, cyclic vectors, and Frobenius forms

DOI10.1016/S0024-3795(97)80005-5zbMath0877.65022MaRDI QIDQ1361771

Paul Camion, Daniel Augot

Publication date: 8 December 1997

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

complexityiterative algorithmcharacteristic polynomialfactorizationminimal polynomialcyclic vectorFrobenius formshift Hessenberg matrix

Mathematics Subject Classification ID

Related Items (4)

Algorithms for finding the minimal polynomials and inverses of resultant matrices ⋮ Linear recurrent cryptography: Golden-like cryptography for higher order linear recurrences ⋮ Computing Minimal Polynomials of Matrices ⋮ The RCH method for computing minimal polynomials of polynomial matrices

Uses Software

• AXIOM

Cites Work

• Some asymptotic results on finite vector spaces
• A deterministic construction of normal bases with complexity \(O(n^ 3+n\log n\log(\log n)\log q)\)
• Computing Frobenius maps and factoring polynomials
• Constructing normal bases in finite fields
• Nearly Optimal Algorithms for Canonical Matrix Forms
• On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials
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