Computing the Kalman form
<|reference_start|>Computing the Kalman form: We present two algorithms for the computation of the Kalman form of a linear control system. The first one is based on the technique developed by Keller-Gehrig for the computation of the characteristic polynomial. The cost is a logarithmic number of matrix multiplications. To our knowledge, this improves the best previously known algebraic complexity by an order of magnitude. Then we also present a cubic algorithm proven to more efficient in practice.<|reference_end|>
@article{pernet2005computing,
    title={Computing the Kalman form},
    author={Cl'ement Pernet (LMC - IMAG), Aude Rondepierre (LMC - IMAG), Gilles
  Villard (LIP)},
    journal={arXiv preprint arXiv:cs/0510014},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0510014},
    primaryClass={cs.SC math.OC}
}