The orthogonal Rayleigh quotient iteration (ORQI) method (Q1855429)

Under a new name we find here the method of inverse iterations [cf. \textit{J. H. Wilkinson}, The algebraic eigenvalue problem, Clarendon, Oxford (1965; Zbl 0258.65037)]. The author performs its error analysis and emphasizes that although the ``local'' rate of its convergence is cubic, a difficulty may be encountered in a ``global'' setting where, in principle, the residual function may possess a saddle point. After one avoids this trap, the efficiency of the algorithm is kept reasonable by performing the necessary re-orthogonalizations ``selectively'' and by working with the band matrices possessing a narrow bandwith.