Theoretical error bounds on the convergence ofthe
نویسنده
چکیده
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. Similar further inequalities are found for the eigenele-ments by using bounds on the acute angle between the exact eigenvectors and the Krylov subspace spanned by x0; Ax0; ; A n?1 x0, where x0 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.
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