Theoretical error bounds on the convergence of the Lanczos and block-Lanczos methods (Q1972461)

New theoretical error bounds on the convergence of the Lanczos and block Lanczos methods are established. Similar results are found for the eigenelements by using bounds on the acute angle between the exact eigenvectors and the Krylov subspace spanned by \(x_0,Ax_0,\dots, A^{n-1}x_0\), where \(x_0\) is the initial starting vector of the process. Numerical experiments compare the actual rates of convergence with theoretical bounds.