New iterative algorithm on a kind of nonsymmetric linear systems

We present the pre-symmetrizers for the nonsymmetric linear systems arising from the discretization of the second order non-scalar nonself-adjoint elliptic equations. Combining these pre-symmetrizers with the CG method, the new algorithm, LRSCG algorithm is presented. The numerical results show that our LRSCG algorithm is better than the well known GMRES algorithm and its symmetrized algorithm, i.e., SGMRES algorithm for these nonsymmetric linear systems.