The influence of orthogonality on the Arnoldi method (Q1976921)

Error bounds for five orthogonalization methods and the Arnoldi method are summarized. It is shown that quality of the eigensolvers depends on the orthonormality of the computed basis. It is also shown that the stopping criterion based on the backward error and the value computed using the Arnoldi method can differ because of the loss of orthonormality of the computed basis of the Krylov subspace. A bound that quantifies this difference is given. Results of some computational experiments are also given.