Practical use of the symmetric Lanczos process with re-orthogonalization

Several extreme eigenvalues and vectors of large symmetric matrices can often be found to machine accuracy by carrying out far less than the full number of steps of the Lanczos process. To prove the accuracy of such results a rounding error analysis of the process with re-orthogonalization is given here. It is found that a stopping criterion has to be introduced to obtain a priori error bounds.