Dealing with linear dependence during the iterations of the restarted block Lanczos methods (Q5934350)

Several ways of handling linear dependence inside the block or band of a block Lanczos algorithm are compared. It is shown that it is necessary to introduce a random direction into the block after linear dependence is discovered, in order to prevent reccurrence of linear dependence after an implicit restart. This is also necessary to make sure a sufficient number of independent eigenvectors are computed to a multiple eigenvalue.