An Error Analysis of a Unitary Hessenberg QR Algorithm

Authors:
Michael Stewart
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2006

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Abstract

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 QHHQ 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.