A New Proof of Global Convergence for the Tridiagonal $QL$ Algorithm
W. Hoffmann, Beresford Ν. Parlett · SIAM Journal on Numerical Analysis · 1978
By exploiting the relation of the $QL$ algorithm to inverse iteration we obtain a proof of global convergence which is more conceptual and less computational than previous analyses. The proof uses a new, but simple, error estimate for the first step of inverse iteration.