When multicomponent, multistage separation problems are solved on para
llel computers by successive linearization methods, the solution of a
large sparse linear equation system becomes a computational bottleneck
, since other parts of the calculation are more easily parallelized. W
hen the standard problem formulation is used, this system has a block-
tridiagonal form. It is shown how this structure can be used in parall
elizing the sparse matrix computation. By reformulating the problem so
that it has a bordered-block-bidiagonal superstructure, it can be mad
e even more amenable to parallelization. These strategies permit the u
se of a two-level hierarchy of parallelism that provides substantial i
mprovements in computational performance on parallel machines.