Spectral Perturbation Bounds for Positive

Let H and H + H be positive deenite matrices. It was shown by Barlow and Demmel, and Demmel and Veseli c that if one takes a component-wise approach one can prove much stronger bounds on i (H)== i (H++H) and the components of the eigenvectors of H and H++H than by using the standard norm-wise perturbation theory. Here a uniied approach is presented that improves on the results of Barlow, Demmel and Veseli c. It is also shown that the growth factor associated with the error bound on the components of the eigenvectors computed by Jacobi's method grows linearly (rather than exponentially) with the number of Jacobi iterations required for convergence.