Theoretical error bounds on the convergence of the Lanczos and block-Lanczos methods

In this paper, the new theoretical error bounds on the convergence of the Lanczos and the block-Lanczos methods are established based on results given by Saad [I]. Similar further inequalities are found for the eigenelements by using bounds on the acute angle between the exact eigenvectors and the Krylov subspace spanned by to, Ax(0),..., A(n-1)x(0), where x(0) is the initial starting vector of the process. The same analysis is extended to the block-lanczos method. Several numerical experiments are presented in order to permit a comparison between the actual rates of convergence of the Lanczos method with the theoretical error bounds. (C) 1999 Elsevier Science Ltd. All rights reserved.