  Deflation techniques for Krylov subspace methods have seen a lot of attention
in recent years. They provide means to improve the convergence speed of these
methods by enriching the Krylov subspace with a deflation subspace. The most
common approach for the construction of deflation subspaces is to use
(approximate) eigenvectors, but also more general subspaces are applicable.
  In this paper we discuss two results concerning the accuracy requirements
within the deflated CG method. First we show that the effective condition
number which bounds the convergence rate of the deflated conjugate gradient
method depends asymptotically linearly on the size of the perturbations in the
deflation subspace. Second, we discuss the accuracy required in calculating the
deflating projection. This is crucial concerning the overall convergence of the
method, and also allows to save some computational work.
  To show these results, we use the fact that as a projection approach
deflation has many similarities to multigrid methods. In particular, recent
results relate the spectra of the deflated matrix to the spectra of the error
propagator of twogrid methods. In the spirit of these results we show that the
effective condition number can be bounded by the constant of a weak
approximation property.
