ScaLAPACK contains a pair of routines for solving systems
which are narrow banded and diagonally dominant by rows. Mathematically,
the algorithm is block cyclic reduction. The ScaLAPACK implementation
can be improved using incomplete, rather than complete block
cyclic reduction. If the matrix is strictly dominant by rows, then it is possible
to bound the truncation error directly in terms of the dominance
factor and the size of the partitions. Our analysis includes new results
applicable in our ongoing work of developing an efficient parallel solver.