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-m 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 nonsymmetric cases are analyzed.