An error analysis of a unitary Hessenberg QR algorithm
Several direct implementations of the QR algorithm for a unitary Hessenberg matrix are numerically unstable. In this paper we give an analysis showing how the instability in a particular rational form of the algorithm specialized to the case of a unimodular shift comes from two sources: loss of accuracy due to cancellation in a particular formula and a dynamic instability in the propagation of the normalization conditions on the Schur parameters and complementary parameters used to represent...[Show more]
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