Comments on “Multiphase systolic algorithms for spectraldecomposition” [and reply]

Comments that the paper by Liu and Yao (see ibid., vol.40, no.1, p.190, 1992) presented an efficient algorithm for spectral decomposition, but the parallel algorithm and architecture for the Hessenberg reduction has a problem. The matrix obtained from the unitary similarity transformation is not necessarily a Hessenberg matrix. The authors reply that the Hessenberg reduction described is not in the Hessenberg form. Only the first column is in its proper form. There are many ways to overcome such a problem. One simple way is to use the multiphase rectangular systolic array