Analysis of the symmetric Lanczos algorithm with reorthogonalization methods (Q1067356)

An error analysis of the symmetric Lanczos algorithm in finite precision arithmetic is presented. A backward error analysis shows that semiorthogonality among the Lanczos vectors is enough to guarantee the accuracy of the computed quantities up to machine precision. The results are extended to the more general case of the Lanczos algorithm with a semiorthogonalization strategy. A new reorthogonalization method called partial reorthogonalization is introduced.