A block version of the nonsymmetric Lanczos method is straightforward, but has many pitfalls awaiting the unwary implementor. Bai studied a simple implementation of the block Lanczos method . Aliaga et al. generalized Ruhe's band Lanczos implementation to the nonsymmetric case . This is presented in §7.10.
The ABLE method for nonsymmetric eigenvalue problems proposed in this section was presented by Bai, Day, and Ye . ABLE also implements a block version of the algorithm presented in [104,105], to monitor the biorthogonality loss and maintain semi-biorthogonality among the computed Lanczos vectors. A so-called -step biorthogonal Lanczos method was proposed by Kim and Chronopoulus  for better data locality on parallel vector computers.