The use of a refined error bound when updating eigenvalues of tridiagonals (Q1094092)

For computing some eigenvalues of a given symmetric matrix A the Lanczos algorithm is used. It provides a nested sequence of tridiagonal matrices \(T_ j\), whose eigenvalues approximate those of A. The eigenvalues of \(T_ j\) tend to stagnate quite early (as functions of j). An algorithm (ANALYZE T) is described, which is a part of the inner loops of the Lanczos algorithm, and which monitors the convergence behaviour of the Ritz values. It helps e.g. to avoid the so called misconvergence.