In this paper we discuss the problem of computing eigenvectors for matrices in
real Schur form using parallel computing. We develop a new parallel algorithm
and report on the performance our our MPI based implementation. We have im-
plemented a new parallel algorithm for scaling during the backsubstitution phase.
We have increased the arithmetic intensity by interleaved the compution of several
eigenvectors and by merging the backward substitution and the back-transformation
of the eigenvectors.