On the convergence rate of the QL algorithm with Wilkinson's shift (Q1111335)

Let T be a symmetric tridiagonal matrix with distinct eigenvalues, and let \(\lambda_ i\) denote the distinct eigenvalues of T in increasing order. It is proved in this note that if \(\lambda_ i\) satisfies \(| \lambda_{i-1}-\lambda_ i| \neq | \lambda_{i+1}-\lambda_ i|\), then the convergence rate of the QL algorithm with Wilkinson's shift, applied to T, is better than cubic.