Convergence of the tridiagonal QR algorithm Original Research Article

By use of the three-term recurrence relation, an elementary and constructive proof is given for the global convergence of the symmetric tridiagonal QR algorithm with Wilkinsonʹs shift. It is further illustrated why the asymptotic rate of convergence is essentially cubic, as has long been observed in numerical experiments. A general mixed shift strategy with global convergence and cubic rate is also presented.