Improved random perturbation intervals of symmetric eigenvalue problem

In this paper, by transforming the symmetric random perturbed matrix into a special form and using the result from Li and Li (2005) [7], we first present an improved random perturbation interval. Under the random perturbation in the interval, the simple eigenvalue of the original matrix is still simple. Then, we extend the result to the case of several eigenvalues. Finally, numerical experiments are given to illustrate the obtained results.