Toward improved uses of the conjugate gradient method for power system applications

H. Dag, F.L. Alvarado
1997 IEEE Transactions on Power Systems  
The conjugate gradient method has been suggested as a better alternative to direct methods for the solution of certain large sparse linear systems A x = b, where A is symmetric and positive de nite. E ciency considerations often require that the conjugate gradient method be accelerated by preconditioning a linear transformation of A. One of the most widely used preconditioners is based on the incomplete LU factors of A. P ositive de nite preconditioner matrices assure convergence. However, the
more » ... ence. However, the incomplete factorization for a symmetric and positive de nite matrix is not necessarily positive de nite. This paper provides signi cant theoretical insights into the conjugate gradient method for matrices arising from several classes of power systems problems. The paper also presents a new preconditioner based on a one-time complete factorization that is guaranteed to be positive de nite.
doi:10.1109/59.630475 fatcat:3r4gr33rp5dhhiazxxjjfvvbby