  The discretization of convection-diffusion equations by implicit or
semi-implicit methods leads to a sequence of linear systems usually solved by
iterative linear solvers such as GMRES. Many techniques bearing the name of
\emph{recycling Krylov space methods} have been proposed to speed up the
convergence rate after restarting, usually based on the selection and retention
of some Arnoldi vectors.
  After providing a unified framework for the description of a broad class of
recycling methods and preconditioners, we propose an alternative recycling
strategy based on a singular value decomposition selection of previous
solutions, and exploit this information in classical and new augmentation and
deflation methods. The numerical tests in scalar non-linear
convection-diffusion problems are promising for high-order methods.
