Before revision:  For decomposing flows H\!K  (t), the algorithm decomposes the given dense matrix A conformally into diagonal blocks as H\!K in U^*AU = \text { diag} (A_j) for a unitary matrix U . It then computes the field of values boundaries separately for each diagonal block A_j using the fast ZNN parameter varying flow eigenvalue method.
After revision:  For decomposing flows H\!K (t), the algorithm decomposes the given dense matrix A conformally into diagonal blocks as H\!K in U^*AU = \text { diag} (A_j) for a unitary matrix U . It then computes the field of values boundaries separately for each diagonal block A_j using the path following ZNN eigenvalue method.