An Error Analysis of a Unitary Hessenberg QR Algorithm
Michael Stewart · SIAM Journal on Matrix Analysis and Applications · 2006
This paper proves the stability of a variant of Gragg's unitary Hessenberg QR algorithm (UHQR). It is shown that a single UHQR iteration with numerically unimodular shift applied to the Schur parameters and complementary parameters of a unitary Hessenberg matrix H gives computed parameters for Q H HQ that are close to those obtained from a perturbed set of parameters using a perturbed shift with no numerical error. The perturbations of the parameters and the shift are bounded.