- Because of roundoff errors, some eigenvalues can appear more than once.
- This is caused by the short recurrence in Lanczos, as opposed to the full orthogonalization process in Arnoldi.
- This does create difficulties in practice.
- However, several modifications to Lanczos can be made to address this problem.
Algorithm for the Lanczos process, Algorithm for the Arnoldi process, Convergence of Lanczos eigenvalues for symmetric matrices, Convergence of Lanczos inner eigenvalues