Applicable to strictly diagonally dominant, or symmetric positive definite matrices. Parallelization properties depend on structure of the coefficient matrix. This is a special case of the SOR method, obtained by choosing . Parallelization properties are the same as those of the Gauss-Seidel method. Applicable to symmetric positive definite systems.
Inner products act as synchronization points in a parallel environment.
Further parallel properties are largely independent of the coefficient matrix, but depend strongly on the structure the preconditioner. Applicable to nonsymmetric matrices. In order to limit the increasing storage requirements and work per iteration step, restarting is necessary. The number of inner products grows linearly with the iteration number, up to the restart point. In an implementation based on a simple Gram-Schmidt process the inner products are independent, so together they imply only one synchronization point.