On the randomized error of polynomial methods for eigenvector and eigenvalue estimates
In this paper we consider the problem of estimating the largest eigenvalue and the corresponding eigenvector of a symmetric matrix. In particular, we consider iterative methods, such as the power method and the Lanczos method. These methods need a starting vector which is usually chosen randomly. We analyze the behavior of these methods when the initial vector is chosen with uniform distribution over the unit n-dimensional sphere. We extend and generalize the results reported earlier. In particular, we give upper and lower bounds on the ii, norm of the randomized error, and we improve previously known bounds with a detailed analysis of the role of the multiplicity of the largest eigenvalue. (C) 1997 Academic Press.
randomized error power and lanczos methods eigenvalues and eigenvectors random start