A new look at the Lanczos algorithm for solving symmetric systems of linear equations

AbstractSimple versions of the conjugate gradient algorithm and the Lanczos method are discussed, and some merits of the latter are described. A variant of Lanczos is proposed which maintains robust linear independence of the Lanczos vectors by keeping them in secondary storage and occasionally making use of them. The main applications are to problems in which (1) the cost of the matrix-vector product dominates other costs, (2) there is a sequence of right hand sides to be processed, and (3) the eigenvalue distribution of A is not too favorable