We are able to get substantially better speedups with the parallel Gauss-Seidel algorithm than with the parallel direct methods for power systems networks, although the only matrix types where there is assurance of convergence for Gauss-Seidel solvers are diagonally dominant and positive definite matrices. Choleski-based linear solvers encountered the worst parallel performance, and are limited to matrix forms where Gauss-Seidel convergence is assured. Due to guarantees of convergence for the Gauss-Seidel algorithm for positive definite or diagonally dominate matrices and the relative performance for the parallel Choleski solver, there is potential for significant algorithmic speedup by selecting the Gauss-Seidel for solving those power systems network matrices that could also use Choleski factorization. We have shown that the applications provide good estimates of starting points for the iterative methods, so convergence appears to be sufficiently rapid that algorithmic speedups of as great as ten may be possible. For those applications that require LU factorization, more information concerning iterative solver convergence would be required in addition to the rate of convergence for real power systems applications data before decisions could be made concerning the selection of direct versus iterative methods.