Critical to the performance of an iterative linear solver is the
convergence of the technique for a given data set. We have applied
our solver to sample positive definite matrices that have actual power
networks as the basis for the sparsity pattern, and random values for
the entries. We have examined convergence for various matrices and
various matrix orderings. A sample of the measured convergence data
is presented in table 1. This table presents the total
error for an iteration, and the minimum and maximum values encountered
that iteration. All initial values, , have been
defined to equal
. Convergence is rather rapid, and after four
iterations, total error equals
. Consequently,
only a few iterations are required for reasonable convergence with
this procedure on this data. We hypothesize that this good
convergence rate is in part due to having good estimates of the initial
starting vector. For actual solutions of power systems load flows,
this solver would be used within an iterative non-linear solver, so
good estimates of starting points for each solution also will be
readily available.
Table 1: Convergence for EPRI-6K Data ---