In this paper, the performance of the five kinds of parallel
re-orthogonalization methods by using the Gram-Schmidt (G-S) method is
reported. Parallelizm of the re-orthogonalization process depends on
the implementation of G-S orthogonalization process, i.e. Classical
G-S (CG-S) and Modified G-S (MG-S). To relax the parallelizm problem,
we propose a new hybrid method by using both the CG-S and MG-S. The
HITACHI SR8000 of 128 PEs, which is a distributed memory super-computer, is
used in this performance evaluation.