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Browsing by Subject "QR algorithm"

Browsing by Subject "QR algorithm"

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  • An extended Hessenberg form for Hamiltonian matrices 
    Ferranti, Micol; Iannazzo, Bruno; Mach, Thomas; Vandebril, Raf (Calcolo, 2016-06-01)
    A unitary symplectic similarity transformation for a special class of Hamiltonian matrices to extended Hamiltonian Hessenberg form is presented. Whereas the classical Hessenberg form links to Krylov subspaces, the extended ...
  • Fast and backward stable computation of roots of polynomials 
    Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S. (SIAM Journal on Matrix Analysis and Applications, 2015)
    A stable algorithm to compute the roots of polynomials is presented. The roots are found by computing the eigenvalues of the associated companion matrix by Francis's implicitly shifted QR algorithm. A companion matrix is ...
  • Roots of Polynomials: on twisted QR methods for companion matrices and pencils 
    Aurentz, Jared L.; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S. (arXiv, 2016-11-08)
    Two generalizations of the companion QR algorithm by J.L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analysis and Applications, 36(3): 942--973, 2015, to compute the roots of a polynomial are ...