  We present an eigenspectrum partitioning scheme without inversion for the
recently described real-space electronic transport code, TRANSEC. The primary
advantage of TRANSEC is its highly parallel algorithm, which enables studying
conductance in large systems. The present scheme adds a new source of
parallelization, significantly enhancing TRANSEC's parallel scalability,
especially for systems with many electrons. In principle, partitioning could
enable super-linear parallel speedup, as we demonstrate in calculations within
TRANSEC. In practical cases, we report better than five-fold improvement in CPU
time and similar improvements in wall time, compared to previously-published
large calculations. Importantly, the suggested scheme is relatively simple to
implement. It can be useful for general large Hermitian or weakly non-Hermitian
eigenvalue problems, whenever relatively accurate inversion via direct or
iterative linear solvers is impractical.
