Cullum [90] has devised a way to weed out such extra
copies and spurious values. She takes the tridiagonal matrix and another
, which is obtained from
by deleting the first row and column.
All eigenvalues of
that are very close to eigenvalues of
need special consideration. If such an eigenvalue is a multiple
eigenvalue of
, keep one of them and discard the rest as copies,
remembering that an unreduced tridiagonal matrix by definition has only
simple eigenvalues. If a simple eigenvalue of
is also an eigenvalue
of
, it is spurious and should be discarded.