Analysis of augmented Krylov subspace methods

Residual norm estimates are derived for a general class of methods based on projection techniques on subspaces of the form K_m + W, where K_1n is the standard Krylov subspace associated with the original linear system and W is some other subspace. These '"augmented Krylov subspace methods" include eigenvalue deflation techniques as well as block-Krylov methods. Residual bounds are established which suggest a convergence rate similar to one obtained by removing the components of the initial residual vector associated with the eigenvalues closest to zero. Both the symmetric and nonsynimetric cases are analyzed.