ABSTRACT
As noted in the references the unitary Hessenberg QR algorithm is fundamental for statistical signal analysis, as is the closely related inverse algorithm (iuhqr). These algorithms are analogous with algorithms, tqr and itqr, for real symmetric tridiagonal matrices. No claim of numerical stability for uhqr was made when it was introduced in 1986. Indeed, an open problem was to make uhqr perform as well as tqr. Here we introduce a device which appears, on the basis of a large number of experiments, to solve the problem. However, given the history of tqr, we must say that this fact awaits proof.
