A note on backward perturbations for the hermitian eigenvalue problem

Through different orthogonal decompositions of computed eigenvectors we can define different Hermitian backward perturbations for a Hermitian eigenvalue problem. Certain optimal Hermitian backward perturbations are studied. The results show that not all the optimal Hermitian backward perturbations are small when the computed eigenvectors have a small residual and are close to orthonormal.Dedicated to Åke Björck on the occasion of his 60th birthdayThis work was supported by the Swedish Natural Science Research Council under Contract F-FU 6952-302 and the Department of Computing Science, Umeå University.