The convergence of diagonal elements of an irreducible symmetric tridiagonal matrix under QL algorithm with some kinds of shift is discussed. It is proved that if α₁—σ→0 and βj→0, j = 1, 2, ···, m, ...

In this paper a new algorithm for reducing an arbitrary real square matrix to tri-diagonal form using real similarity transformations is described. The method is essentially a generalization of a ...