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 ...
Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S.(Electronic Transactions on Numerical Analysis, 2015)
A fast Fortran implementation of a variant of Gragg's unitary Hessenberg QR algorithm is presented. It is proved, moreover, that all QR- And QZ-like algorithms for the unitary eigenvalue problems are equivalent. The algorithm ...
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 ...
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