Next: Selective Reorthogonalization.
We could play it safe and do a full reorthogonalization either by
modified or classical Gram-Schmidt, in the latter case computing the
orthogonalization coefficients in a vector
and then subtracting
to get the improved vector . If the norm is decreased by a
nontrivial amount, say
this will have to be repeated, but this will hardly ever happen when
treating properly computed Lanczos vectors.