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Convergence Rate

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 ---  



David P. Koester
Sun Oct 22 15:29:26 EDT 1995