In the symmetric case, the purging process is
essentially the same as the locking process just described.
However, instead of keeping the deflated Ritz vector and value, they are
simply discarded. After this, we are left with a -step factorization
Observe that there is no requirement that be an accurate eigenvector for . It is only necessary for the residual to meet a componentwise accuracy condition that we shall discuss in the next subsection. Moreover, there is no need for the last element of the eigenvector to be small in the case of purging. However, when it is not small, the implicit restart mechanism with exact shifts will suffice to purge . Finally, this procedure is valid in complex arithmetic with minor notational modifications.