Implicitly restarted and deflated GMRES (Q1817793)

The paper presents a deflation method that takes advantages of the implicitely restarted Arnoldi (IRA) method, by extracting a generalized minimal residual (GMRES) solution from Krylov basis computed within the Arnoldi process of the IRA method itself. The deflation is well suited because it is done with eigenvectors associated to the eigenvalues that are closest to zero, which are approximated by IRA very quickly. The procedure is adapted to the full orthogonal method algorithm by means of a slight modification, and then to the GMRES method. IRA enables the user to reduce the number of matrix-vector products, while keeping a low storage.